Generalization of the definitions of the stability of the socio-economic system. The stability of a complex socio-economic system at the mathematical level Recommended list of dissertations

Chapter 10

10.1. General scheme of sustainability

A huge number of works are devoted to the problems of cognition, including in the socio-economic field. However, this does not mean that everything in this area has already been said. And it is advisable to talk about some provisions again and again until they become generally known.

This book proposes, studies and discusses econometric models of socio-economic phenomena and processes, and also considers the general requirements that naturally apply to such models. Ideally, each such model should be considered as an axiomatic theory. In this ideal case, the creation and use of the model occurs in accordance with the well-known triad "practice - theory - practice". Namely, first some mathematical objects are introduced that correspond to the real objects of interest to the researcher, and on the basis of ideas about the properties of real objects, the properties of mathematical objects necessary for successful modeling are formulated, which are accepted as axioms. Then the axiomatic theory develops as a part of mathematics, out of touch with ideas about real objects. At the final stage, the results obtained in the mathematical theory are interpreted meaningfully. Statements about real objects are obtained, which are consequences of those and only those of their properties that were previously axiomatized.

The econometric models considered in this book are also expressed in mathematical language, they are studied by means of mathematics without involving meaningful socio-economic considerations, and the conclusions are interpreted in the language of the corresponding subject area, i.e. meaningful.

After constructing a mathematical model of a real phenomenon or process, the question of its adequacy arises. Sometimes the answer to this question can give an experiment. The discrepancy between the model and experimental data should be interpreted as a sign of the inadequacy of some of the accepted axioms. However, to test the adequacy of socio-economic models, it is often impossible to set up a decisive experiment, in contrast to, say, physical models. On the other hand, for the same socio-economic phenomenon or process, as a rule, it is possible to compile many possible models, if you like, many varieties of one basic model. Therefore, some additional conditions are needed that would allow them to choose the most suitable ones from the set of possible models and econometric methods for data analysis. In this chapter, as one of these conditions, the requirement is put forward sustainability model and method of data analysis in relation to the allowable deviations of the initial data and the prerequisites of the model or the conditions for the applicability of the method.

Note that in most cases, researchers and practitioners are interested not so much in the models and methods themselves as in the decisions that are made with their help. After all, models and methods are developed in order to prepare solutions. At the same time, it is obvious that decisions, as a rule, are made in conditions of incomplete information. So, any numerical parameters are known only with some accuracy. Introduction to the consideration of possible uncertainties in the initial data requires some conclusions about the stability of the decisions made with respect to these permissible uncertainties.

We introduce the basic concepts according to the monograph .. We assume that there are initial data, on the basis of which solutions. The method of processing (displaying) the initial data into a solution is called model. Thus, from a general point of view, a model is a function that translates the initial data into a solution, i.e. the transition method does not matter. Obviously, any model recommended for practical use should be investigated. for stability relative to the allowable deviations of the original data. Here are some possible applications of the results of such a study:

The customer of the research work gets an idea of the accuracy of the proposed solution;

It is possible to choose the most adequate from many models;

According to the known accuracy of determining the individual parameters of the model, it is possible to indicate the required accuracy of finding the remaining parameters;

The transition to the case of "general position" allows one to obtain results that are stronger from a mathematical point of view.

Examples. For each of the four possible applications listed, various examples have already been given in this book. In econometrics, the accuracy of the proposed solution is related to the scatter of the initial data and the sample size, and methods for estimating the accuracy of the solution for various problems are described above. The choice of the most adequate model is devoted to many considerations in Chapters 4 and 5, related to the discussion of homogeneity and regression models. Rational sample size in statistics of interval data (Chapter 9) proceeds from the principle of equalization of errors, based on the fact that by the known accuracy of determining the individual parameters of the model, it is possible to indicate the required accuracy of finding the remaining parameters. Another example of applying the same concept is finding the required accuracy of parameter estimation in the logistics models discussed in Chapter 5 of the monograph. Finally, the transition to the case of "general position" in econometrics is, in particular, the transition to nonparametric statistics, which is necessary because it is impossible to substantiate the belonging of observational results to one or another parametric family.

Modelers and management theorists consider sustainability to be one of the important characteristics of socio-economic models. In-depth research is being carried out in a number of areas.

The initial study of the effect of a small change in one parameter is commonly referred to as sensitivity analysis. It is usually described by the value of the partial derivative. If the model is given by a differentiable function, then the result of the sensitivity analysis is a vector of partial derivative values at the analyzed point.

The theory of stability of solutions of differential equations has been developed at least since the 19th century. Appropriate concepts have been worked out - stability according to Lyapunov, correctness, deep theorems have been proved. To solve ill-posed problems, Academician of the Academy of Sciences of the USSR A.N. Tikhonov proposed a regularization method in the early 1960s. Models of socio-economic phenomena and processes, expressed with the help of differential equations, can be investigated for stability by applying a well-developed mathematical apparatus.

Sustainability issues have been studied in almost all areas of economic and mathematical methods - and in mathematical programming, and in the theory of queuing (the theory of queues), and in ecological and economic models, and in various areas of econometrics.

Before moving on to specific formulations, let's discuss the "general scheme of sustainability", which provides a conceptual basis for discussing sustainability issues in various subject areas.

Definition 1. The general scheme of stability is an object

Here, is a set called (and interpreted) by the space of initial data; is a set called the solution space. A one-to-one mapping is called a model. These three components of the overall sustainability scheme have already been discussed above.

The remaining two concepts are needed to refine the concepts of proximity in the space of initial data and the space of solutions. Such refinements can be made in different ways. The "weakest" refinement is in the language of topological spaces. Then qualitative conclusions are possible (converges - does not converge), but not quantitative calculations. The most "strong" refinement is in the language of metric spaces. Intermediate option - difference indicators are used (they differ from metrics in that the triangle inequalities are not necessarily satisfied) or the concepts introduced below.

Let d- indicator of stability, i.e. non-negative function defined on subsets At set and such that it follows from Often the stability index d(Y) defined using a metric, pseudo-metric or difference indicator (proximity measure) as the diameter of a set U, those.

Thus, to put it simply, in the solution space, with the help of the stability index, a system of neighborhoods can be formed around the image of the initial data. But first it is necessary to form such a system in the space of initial data.

Let - a set of permissible deviations, i.e. a system of subsets of the set such that each element of the set of initial data and each parameter value from a certain set of parameters corresponds to a subset of the set of initial data, called the set of tolerances at the point X with the parameter value equal to . One can clearly imagine that around the point X a neighborhood of radius is taken.

Definition 2. The index of stability at the point x with the value of the parameter equal to , is the number

In other words, this is the diameter of the image of the set of permissible oscillations for the mapping considered as a model. Obviously, this indicator of stability depends both on the initial data and on the diameter of the set of possible deviations in the initial space. For continuous functions, the stability index is usually called the modulus of continuity.

It is natural to see to what extent the image of the neighborhood of possible deviations narrows down with the maximum possible narrowing of this neighborhood.

Definition 3. The absolute indicator of stability at the point x is the number

If the function f is continuous, and the neighborhoods are exactly those that are discussed in mathematical analysis, then the maximum narrowing means narrowing to a point and the absolute stability index is 0. But in chapters 3 and 9 we encountered completely different situations. In Chapter 3, the neighborhood of the original data was all those vectors that were obtained from the original by transforming the coordinates using the admissible scale transformation, and the admissible scale transformation was taken from the corresponding group of admissible transformations. In Chapter 9, it was natural to understand the neighborhood of the initial data - when describing the sample - as a cube with edges and a center in the original vector. In both cases, the maximum narrowing does not mean narrowing to a point.

It is natural to want to introduce stability characteristics over the entire space. Without going into mathematical subtleties (see the monograph about them), consider a measure on space such that the measure of the entire space is equal to 1 (i.e.

Definition 4. The number

Here we have in mind the so-called Lebesgue integral. The integration is carried out over the (abstract) space of initial data over the measure . Naturally, some intra-mathematical conditions must be met, which econometrics does not need to think about. For the reader unfamiliar with Lebesgue integration, it is enough to mentally replace the integral in the previous formula by the sum (and consider the space as finite, although consisting of a large number of elements).

Definition 5. The maximum absolute indicator of stability is called

It is easy to see that where the supremum is taken over all the measures described above.

Thus, a hierarchy of sustainability indicators for econometric and economic-mathematical models has been constructed. It has been successfully used in research, developed in detail, in particular, in a monograph. In particular, the following definition turned out to be useful.

Definition 6. A model f is called absolutely stable if where is the maximum absolute stability index.

Example. If the stability indicator is formed using a metric, the set of permissible deviations is the set of all neighborhoods of all points in the initial data space, then the 0-stability of the model f"is equivalent to the continuity of the model f on the set.

The main problem in the overall stability scheme - examination -stability of the given model f with respect to the given system of permissible deviations .

The following two generalizations of the main problem are often useful.

Problem A (characterization of stable models). Given the initial data space , the solution space , the stability index d, the set of allowable deviations, and a non-negative number . Describe a sufficiently wide class of -stable models f. Or: find all -stable models among models with given properties, i.e. included in this set of models.

Problem B (characterization of systems of permissible deviations). Given the initial data space , the solution space , the stability index d, the model f and a non-negative number . Describe a sufficiently wide class of tolerance systems with respect to which the model f is -stable. Or: find all such systems of tolerances among sets of tolerances that have given properties, i.e. included in this set of sets of permissible deviations.

It is clear that problems A and B can be considered not only for the stability index, but also for other stability indicators just introduced, namely,

The language of the general stability scheme makes it possible to describe specific problems of specialized theories of stability in various fields of research, to single them out as the main elements in them, to pose problems of type A and B. In this language, problems of the theory of stability of solutions of differential equations, the theory of robustness of statistical procedures, problems of the adequacy of the theory measurements (see Chapter 3), the achievable accuracy of calculations in statistics of interval data (see Chapter 11) and in logistics (see monograph), etc.x

Thus, the general stability scheme naturally includes the classical concepts of Lyapunov's stability theory. At the same time, it should be noted that this scheme provides a general approach to various stability problems, primarily in econometric and economic-mathematical formulations, it provides a system of concepts that in each specific case should be adapted to the problem being solved.

Until now, for definiteness, we have been talking about permissible deviations in the space of initial data. Often it is necessary to talk about deviations from the assumptions of the model. From a purely formal point of view, it suffices to expand the concept of "initial data" to a pair (x, f), those. by including the "former" model as the second element of the pair. All other definitions remain unchanged. Deviations in the decision space are no longer caused only by deviations in the original data x, but also deviations from the assumptions of the model, i.e. deviations f. We will need this consideration in the next subsection of this chapter, which is devoted to the robustness of statistical procedures.

It is also natural to consider various asymptotic statements in econometric theory (the third point of this chapter) as problems of stability. If a quantity tends to a limit as the sample size grows without limit, then in terms of the general stability scheme, this means that it is 0-stable in the corresponding pseudometric (see the discussion of asymptotic Lyapunov stability above). From a substantive point of view, the use of the term "stability" in such a situation seems to be quite justified, since the value under consideration changes little when the sample size changes.

For strategic management, the problem of the planning horizon is very important (for more details, see the tutorial). Obviously, the type of optimal solutions depends on the predetermined length of the interval for which the optimal plan is built (ie, on the planning horizon). This means that it is necessary to justify the choice of the planning horizon. It is irrational to accept it as infinite, since it is quite clear that in some 100 years the productive forces and production relations will be completely different than at present, and it is not advisable to try to take them into account for decision-making at the present time. How to be? This is discussed in the fourth paragraph of this chapter.

UDC 338.46

development of the theory of sustainability of socio-economic systems

Sulpovar L.B.,

doctor of economic sciences, professor,

FGOUVPO "Russian State University of Tourism and Service", Moscow

The author discusses the theoretical, scientific and practical challenges of sustainable development in the socio-economic systems. The article establishes principles for the sustainable development, describes local sustainability indicators, which should define the stability integral indicator.

The article deals with theoretical and scientific-practical problems of ensuring the sustainable development of socio-economic systems. The principles of sustainable development of systems are substantiated, local indicators of sustainability are proposed, on the basis of which the integral indicator of sustainability should be determined.

Key words: sustainability, socio-economic systems, sustainability indicators.

The global financial crisis had a negative impact on all the main institutions of the market economy: the manufacturing sector, the banking system, foreign economic activity, and the social sphere. Under these conditions, the problem of ensuring the sustainable development of all market entities has acquired particular relevance.

The theory of stability of socio-economic systems originally emerged as a branch of other branches of knowledge (mathematics, systems theory, cybernetics, etc.) and absorbed a number of interdisciplinary categories. In economic theory, the problems of sustainability of economic systems, until recently, were considered mainly from the point of view of the result, the outcome of their functioning, as well as from the standpoint of the principles formulated by mathematics.

The sustainability of a socio-economic system differs significantly from technical and physical sustainability. For economic theory, it is characteristic to consider the problems of sustainability simultaneously with the problems of reproduction and market equilibrium. K. Marx, for example,

considered natural disequilibrium between the main divisions of social production. If this natural phenomenon is carried out, there is no balance, this is the sustainable nature of the reproduction of the economic system of the industrial type. If the law is violated and the system is in a state of equilibrium, then there is no stability of expanded reproduction.

Steadily reproducing instability is the law of the market economy. The loss of stability of the system is observed during the period of crisis, the transition of the system from one state to another. Developing this idea in Capital, K. Marx emphasizes that formal metamorphosis creates the general possibility of a crisis: “But one cannot say that the abstract form of the crisis is the cause of the crisis. If one asks about its cause, what one wants to know is precisely why its abstract form, the form of its possibility, is transformed from possibility into actuality.

The first mathematical model of general economic equilibrium was proposed at the end of the 19th century. L. Walras and A. Marshall

THEORY QUESTIONS

considered instability in the context of a set of equilibrium points: an unstable position is invariably located between two stable ones. Since the 1930s, the problem of equilibrium stability has been studied by J. Hicks, P. Samuelson, K. Arrow, F. Khan, T. Negishi, L. Mackenzie, X. Uzawa and others.

J. Hicks proposed a stability criterion, according to which an increase in the price of a given product should cause a decrease in excess demand for it, and this effect is stronger than the possible secondary effect associated with the indirect influence of the prices of other goods, the change in which was generated by a change in demand for them as a result of a change in the price of the original product.

P. Samuelson proposed his own approach to the analysis of stability; he proceeded from the concept of stability as an “attraction” to a certain point, i.e. understood it as a property of the system to return to the equilibrium trajectory after changing the initial conditions. He turned to the dynamic characteristics of the process of "finding the price", namely, to the dependence that connects the rate of change in the price of a product and the amount of excess demand for it.

One of the directions investigating the problems of sustainability is institutionalism. Representatives of this trend believe that the stability of the system is violated when internal and external factors undermine the compatibility and mutual "cohesion" of institutions. This is followed by a period of radical changes in society and the economy.

The stability of the entire economic system, according to the views of institutionalists, depends on a combination of a measure of homogeneity and heterogeneity of institutional units. Complete homogeneity leads to inhibition of development and to the destruction of the system, while complete heterogeneity leads to an increase in entropy and chaos. Based on this, excessive internal diversification is no less dangerous than complete homogeneity.

“Institutional traps”, which are understood as inefficient stable norms, inefficient institutions, have a special impact on the stability of the system. The term "institutional trap" is also applied to inefficient equalizations.

weights generated by the corresponding norm. Stability in this context has the usual meaning. It means that for small perturbations, the system remains in an institutional trap, perhaps only slightly changing its parameters, and returns to its previous state as soon as the source of the perturbation is removed.

In the case under consideration, there is a negative, unfavorable stability for the economic system. This state is unfavorable for the participants in the system, but the refusal of an individual subject from the established rules leads to a deterioration in his condition. The main reason for the persistence of institutional traps is the lack of coordination.

At the present stage of studying the stability of socio-economic systems, scientists are increasingly expressing ideas about the need to synthesize orthodox and evolutionary economics for a more complete study of the problems of stability and "balance-disequilibrium" of economic systems.

The focus of research over the past two decades is no longer stability or instability per se, but the question of the relationship between these categories, which is transforming into the problem of the relationship between stability and instability, certainty and uncertainty. The concept of "instability", according to I.Prigozhin, "... is now freed from a negative connotation. Instability can be a condition for a stable dynamic world.

Phenomena that were perceived by science as secondary (chaos, randomness, inertia) acquire a leading and positive meaning, especially since, in the end, instability is nothing more than a dialectical definition that arises on the basis of stability as its opposite. Development in general, and sustainable development in particular, is possible only as a result of the appearance of instability.

The movement from an unstable state caused by external influences to a new stable state that meets the changed conditions, this, in essence, is development. The task is to learn to perceive stability in connection with instability, because they are interconnected. In this regard, the study of the problems of transition and transformation is being updated.

Scientists studying the problems of stability of socio-economic systems are increasingly turning to the apparatus of catastrophe theory, non-equilibrium dynamics and synergetics and rely on the study of nonlinear processes in the natural sciences and on the idea of the presence of a certain general algorithm for self-organization and the development of complex systems (E. Erokhina, E. .Knyazeva, I.Prigozhin, I.Shurgalina). However, drawing a parallel between the level of development of natural science and social science causes criticism.

Considerable attention in the study of stability is paid to the problems of chaos. The phenomena of "chaos" and "uncertainty" seem to be new "framework factors", which at the beginning of the 21st century become extremely significant, if not decisive, for the development trends of the world economy and politics. Scientists are making attempts to study stability in conditions of uncertainty and chaos, as well as the process of transition of the economy from one economic order to another through a chaotic state.

Modern analysis of the stability of socio-economic systems often operates with the concept of "structural stability". A feature of this approach is the analysis of a family of trajectories that are “close” to the standard scheme, since structural stability characterizes the qualitative similarity of different systems when different parameters change. At the stage of transition of structural stability of one type to structural stability of a higher type, through the state of structural instability, a new law of irreversible changes comes into force: the higher the level of decomposition of the former structure, the deeper the alternativeness of the development process and the more real the unpredictability of the final result of ongoing events: their completion in accordance with pre-planned scenario.

There is a special relationship between the rate of death of "old" elements and the rate of growth of new elements. If the growth of new elements does not outpace the rate of extinction of "old" elements, the system will retain its structural stability, but with the outstripping growth of emerging elements between new and old elements

functional connections do not have time to form, and the system enters a phase of intensive decomposition of its former structure. With an avalanche-like onset of a state of structural instability, the system becomes extremely sensitive to external influences.

A promising direction is the study of “quasi-stability”, which is possessed by any trajectory that starts near the equilibrium position and remains within the boundaries close to equilibrium without necessarily reaching it. In modern literature, there are options for considering economic systems as "active disequilibrium" .

Of great practical importance is not only the study of the stability of the economic system as a whole, but also its individual elements, for example, financial stability, the stability of social and labor relations, the stability of foreign economic activity, etc. In the 70s of the last century, a separate direction of economic thought appeared, exploring economic stability of the state. It is called "ecostate" ("economic security of state"). Representatives of this direction believe that it is possible to ensure the economic stability of the state only with the economic stability of its structural elements (territories, industries, enterprises).

There is a growing interest in the problems of social sustainability, incl. from international organizations. The World Bank's 2003 World Development Report focuses specifically on social sustainability. This is because societies are transforming and will continue to transform over time.

However, it is clear that significant social stresses (in the extreme manifestation - social conflicts) lead to a violation of the accumulation or conservation of all resources, thereby threatening the well-being of all generations and sustainability. The success of this kind of work in the field of stability research is explained by the empirical orientation (both in research methods and in purpose). However, the discovery and understanding of the real patterns of system stability can

be implemented only at the next level of generalization - the system level.

Attempts are being made to develop quantitative criteria for the sustainability of socio-economic systems. At the same time, two main directions are distinguished: the development of indicators, the use of which is possible only for socio-economic systems (for example, the Altman model), and the adaptation of stability indicators used in mathematics and physics.

Often there are attempts to adapt the theories of stability according to Lyapunov and according to Langrange to economic processes. However, researchers note that assessing the stability of socio-economic systems according to Lyapunov at the present stage is practically impossible due to the difficulty of describing restrictions on certain disturbances and the difficulty of taking into account all possible disturbances.

Considerable attention is paid to the problems of not only the sustainability of socio-economic systems, but also their sustainable development. The transition to sustainable development means the creation of a balanced system that combines social justice, environmental (and other) security and economic efficiency. Its main objective is to achieve optimal development results with minimal environmental impact.

At the international level, the problems of sustainability of economic systems that have entered the post-industrial phase of development are being studied. As you know, a post-industrial society is formed on a foundation, the strength of which is due to the close relationship between the progress of technology and the development of the individual. This is what ensures the stability of the emerging system, makes it invulnerable to external destabilizing factors. The economic and political practice of the 1990s shows that at present there are no serious threats to the stability of the Western world. To a large extent, this is facilitated by the growing isolation of the post-industrial community within its main centers - the United States, the European Union and partly Japan, which since the early 1990s have received the rapidly rooted name "the triad" .

Scientists are closely approaching the development of models for the formation of sustainability of socio-economic systems. Particular attention is paid to the problems of stability of the world and national economy in the context of globalization. The need for the development of socio-economic systems of a special kind of dissipative structures that can maintain stability in a turbulent external environment is recognized. This is due to the fact that social design is entering an era of rapidly replacing each other creative models of “one-time use”, which have a short life span, significantly reducing the role of generalizations, individualized in relation to this or that situation outside the spaces of standard constructions and the usual methods of social design. The fundamental advantage in this case turns out to be in the hands of the subjects who control the very process of establishing certain rules of the game in relation to certain changing circumstances. Such an unstable dynamic state of a chaotic, losing its usual structural environment, in which traditional socio-constructions are deprived of support and continue to exist in their previous forms only by inertia, allows only one, special class (“new class”) of dissipative social structures to develop successfully, for which such the state of things is natural. These structures are characterized by adaptability to a dynamic environment and carry the infrastructure of coexistence with chaos and its management.

Thus, modern approaches to the study of the stability of socio-economic systems are characterized by methodological pluralism, a deepening relationship with the natural sciences, attempts to justify the leading role of instability and chaos in economic development, the development of a theory of stability of the constituent elements of the system and a global theory of stability.

The term "sustainability" in relation to socio-economic systems that are subjects of market relations can be formulated as follows: the sustainability of the development of such systems is a state that, under conditions of dynamic

changes in the internal and external environment has a positive tendency to generate income and provides for a long period of retention, and subsequently the expansion of the controlled part of the target market on the basis of constantly developed and implemented investments in production activities.

Methodological principles of sustainable development of socio-economic systems can be divided into general and particular. The general principles include the following:

The principle of responsibility to the future - certain restrictions in the field of exploitation of natural resources;

The principle of partnership - combining the efforts of various parties to achieve the goal;

The principle of observance of the hierarchy of levels - the levels of the sustainable development mechanism: state and regional;

The principle of unity of goals - the activities of all levels of the hierarchy are united by the unity of goals;

The principle of complexity - in order to achieve sustainable development, it is necessary to implement the following support systems: legislative, legal and regulatory, economic, scientific, educational, logistical, personnel, organizational;

The principle of the unity of the organization of legislation is the stability and adequacy of the legislative framework for all types of activities.

In turn, private principles include:

The principle of regularity - providing information about innovations in all related industries;

The principle of efficiency - informing organizations about the most significant innovative achievements in a short time;

The principle of accessibility - the free bringing of innovations to interested organizations;

The principle of reliability - the prevention of distortions or errors in the dissemination of information;

The principle of completeness - information about innovations should be complete and sufficient;

The principle of equality - ensuring equal rights and opportunities in obtaining and access to information for all organizations;

The principle of security is the use of methods and means of protecting information that is a state, official and commercial secret, as permitted by law.

The sustainability of the socio-economic system is a complex and complex category, which includes a number of private (local) indicators that characterize certain aspects of its state and development. The most important of them are the following:

Marketing sustainability - the presence of an unmet need of the target market for products, works and services produced (performed or rendered) by this organization at a certain level of price and quality;

Production sustainability - the presence of the organization's potential ability to produce a volume of production of products, works and services that exceeds breakeven;

Technological sustainability - the ability to consistently ensure a competitive level of quality of manufactured products, work performed and services rendered and based on the use of advanced technology;

Sustainability of technical potential - the ability of fixed assets to produce products, works and services of a competitive level;

Environmental sustainability - the ability of the organization to ensure long-term compliance with the rules, norms and standards for the protection of the environment (MPS, MPEs, MPCs, etc.);

Personnel sustainability - the degree of adaptation of the organization's workforce to production conditions;

Organizational sustainability - compliance of the organizational structure of the organization's management with the conditions of the external and internal environment;

Financial stability - the ability of the organization in the foreseeable future not to have overdue payments on its obligations;

Economic sustainability - the ability of an organization to ensure the most efficient use of all used

my resources (factors of production) in the long run.

All these types of sustainability characterize the state and development of the organization from different angles, while all of them are closely interconnected and affect each other and the dominant indicator - economic sustainability. Only individual types of sustainability taken in a complex make it possible to judge the integral sustainability of the organization's activities and the possibilities for its further development.

The calculated local indicators of the sustainability of the organization's development, the main of which is the indicator of economic sustainability, considered separately from other indicators, make it possible to determine the integral indicator of sustainability and, based on its value, develop the necessary organizational, technical and economic measures to further increase sustainability.

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Shovgenov Tembot Muratovich
Adyghe State University
[email protected]

annotation

The formation of a sustainable socio-economic system should be based on the principles of sustainable development. It should be noted that the current economic situation in Russia, the existing mechanisms for the formation of the financial and economic base of regions and municipalities - all this counteracts the implementation of sustainable development strategies. The article discusses different approaches to assessing the sustainability of socio-economic systems.

Keywords

socio-economic system, sustainable development, region, municipalities, strategy, sustainability

Featured link

Shovgenov Tembot Muratovich

Main aspects of sustainability of regional socio-economic systems// Regional Economics and Management: electronic scientific journal. ISSN 1999-2645. - . Article number: 1107. Publication date: 2007-09-29. Access mode: https://site/article/1107/

Shovgenov Tembot Muratovich
Adyghe State University
[email protected]

Abstract

The formation of a stable socio-economic system should be based on the principles of sustainable development. It should be noted the fact that the current economic situation in Russia, the existing mechanisms of financial and economic base of regions and municipalities - all oppose the implementation of sustainable development strategies. The article discusses different approaches to assessing the sustainability of socio-economic systems.

keywords

socio-economic system, sustainable development, region, municipalities, strategy, sustainability

Suggested Citation

Shovgenov Tembot Muratovich

Key aspects of the sustainability of the regional socio-economic systems. Regional economy and management: electronic scientific journal. . Art. #1107. Date issued: 2007-09-29. Available at: https://website/article/1107/

Russian region is a complex multi-level structure that has internal dynamics and is an essential element of the national economy. Regional economic systems are characterized by a combination of social, economic, environmental, information and other components, the presence of many complex elements, a large number of various connections, the circulation of large flows of material, financial and information resources. In Russia, which is a federal state, the key issues are economic independence, security and sustainable development of the regions.

Socio-economic systems include the world community, unions of states, states, administrative units within the state, branches of the economy, individual enterprises, groups of people.

Theory of sustainability of socio-economic systems, being a derivative of some other branches of knowledge (cybernetics, systems theory, etc.), has absorbed a number of interdisciplinary categories. Among them is the “system”, which is characterized by a hierarchy of organized subsystems, the movement of individual parts and, in the aggregate, development, the presence or lack of development resources. An important concept is “structure”, which is understood as parts of one system that enter into relationships in a certain way. Each system has a potential (resource, capital) that contributes to its development. Development refers to changes occurring in the system, taking a structural, qualitative and quantitative form, or these are changes that reflect the nature of functioning. The socio-economic system is able to evolve from one type to another, in particular, to one in which the consumed resources are restored, reproduced, replaced by others, their consumption is minimized if it is impossible to continue development without non-renewable resources.

The stability of the socio-economic system is significantly different from the technical, physical stability. Since the main characteristic in it is not some equilibrium state and the ability to return to it in the event of disturbing influences, or the preservation of a given trajectory of movement in the case of opposing forces, but the ability to effectively use, autonomously modify the resources of its development, continuously increase the indicators of its positive change without increasing or by minimizing the cost of basic, non-renewable resources.

The formation of a sustainable socio-economic system should be based on principles of sustainable development, the main ones being:

improving the quality of life;

guaranteed health of people;

meeting the basic vital needs of both the population and future generations;

the fight against poverty;

rational structures of production and consumption;

rational use of natural resources;

conservation of ecosystems, protection of the climate and the ozone layer;

ensuring environmental safety;

elimination of all forms of violence against man and nature (prevention of wars, terrorism and ecocide);

global partnership.

In the theory of sustainable development, there are several approaches to assessing the sustainability of socio-economic systems. As the first approach, it is possible to determine the methodology for calculating the indicator " True savings“(Genuine saving), developed by researchers of the World Bank to assess the sustainability of the economy. It defines the welfare of the country in a broader sense than national accounts. The purpose of the indicator is to present "the value of the net change in the whole range of assets that are important for development: productive assets, natural resources, environmental quality, human resources and foreign assets." The adjustment of gross domestic savings is made in two stages. At the first stage, the value of net domestic savings (NDS) is determined as the difference between gross domestic savings (GDS) and the value of the depreciation of produced assets (CFC). In the second step, net domestic savings increase by education spending (EDE) and decrease by natural resource depletion (DRNR) and pollution damage (DME): GS=(GDS-CFC)+EDE-DRNR-DME.

The Genuine Saving approach has advantages over many other types of national calculations because it gives countries uniform, clear, positive or negative numbers. Permanent negative results can be interpreted as the fact that the country is on an unsustainable path, which will lead to negative effects in the long run.

The following approach to assessing sustainability is proposed by Yale and Columbia University for the World Economic Forum in Davos − Calculation of the Environmental Sustainability Index — Environmental Sustainability Index. The index value is calculated using 22 indicators. Each indicator is determined by averaging 2-5 variables, 67 variables are selected in total. Formally, all variables receive equal weight when calculating the index, since there are no generally recognized priorities in ranking environmental problems. The top ten most sustainable countries include Finland, Norway, Canada, Sweden, Switzerland, New Zealand, Australia, Austria, Iceland, Denmark and the United States.

Noteworthy calculation method Index of sustainable economic well-being (Index of Sustainable Economic Welfare) calculated in 1989 by Cobb and Daly (USA) and presented to European countries (Germany in 1991, Great Britain in 1994, Austria, Scotland, Denmark and the Netherlands). It represents the size of GDP per capita, adjusted for the sum of the costs of socio-economic and environmental factors. The development of this index is an attempt to build an aggregated monetary index that is directly comparable to national accounts standards, taking into account important points that are denied in other methods due to their high aggregation. When calculating ISEW variables such as the cost of water pollution, air pollution, noise pollution, loss of agricultural land, compensation to future generations for the loss of non-renewable energy sources, etc. are taken into account.

In a number of countries, such as the USA, Great Britain, Denmark, Portugal and others, a whole system of indicators is used to assess the sustainability of socio-economic systems. One of the most comprehensive systems of indicators of sustainable development was developed by the United Nations Commission on Sustainable Development (UN CSD) in 1996. Four areas were identified: social, economic, environmental and institutional. The selection of indicators was carried out according to the scheme: pressure, state, reaction. The initial list included 134 indicators, then this list was reduced to 60 and a classification by topic was added.

The system has received wide recognition in the world environmental indicators Organization for Economic Cooperation and Development (OECD). The OECD model identifies causal relationships between economic activity and environmental and social conditions and helps policymakers and the public to see the relationship between these areas and develop policies to address these problems.

The abundance of terms describing the concept of "sustainable development", with all the wide palette of interpretations, agree that it takes into account the need to take into account and balance current and future vital needs. The fashion for developing regional (and even municipal) sustainable development programs that began in Russia in the mid-1990s continues to this day. In these programs, the targets are, as a rule, regionally specific and directly focused on using the existing prerequisites for stabilizing and improving the socio-economic situation of the respective territories. At the same time, the question of indicators and criteria of regional stability remains practically open. Methods recommended by the Ministry of Economic Development for determining the level of socio-economic development of regions (in order to identify the asymmetry of the socio-economic situation of the studied administrative-territorial formations - ATO do not eliminate the defect of the universal approach and require adaptive adjustment. It should be noted that the current economic situation in Russia, the current mechanisms for the formation of the financial and economic base of regions and municipalities - all this opposes the implementation of sustainable development strategies. Here, the "selfish" model of behavior is reproduced not by an individual, but by a territorial community of people. Regions are forced to intensify the exploitation of natural resources as the only, in some cases, source of formation budget.

Thus, in order to move Russia towards sustainable development, it is necessary to develop and implement a consistent and effective economic, investment, environmental and regional policy. The transition to sustainable development is a complex and long-term process that affects virtually the entire range of problems of long-term development of both the country as a whole and its individual regions.

Bibliographic list:

Adams R., Performance indicators for sustainable development, Accounting and Business, April, 1999.
Meadows D.H., Meadows D.L., Randers J., Behrens W.W. The limiting to growth. N.Y.: Potomac, 1972.
Bobylev V. Information and methodological basis for the calculation of environmental and economic indicators, Moscow State University, 2000.

References:

Adams R., Performance indicators for sustainable development, Accounting and Business, April, 1999.
Meadows DH, Meadows DL, Randers J., Behrens WW The limiting to growth. N.Y.: Potomac, 1972.
V. Bobylev Information and methodological basis for the calculation of ecological and economic indicators, MSU, 2000.

Generalization of the definitions of the sustainability of the socio-economic system

The concept of sustainable development first came into international use in 1987 after the publication and approval by the UN General Assembly of the report of the Commission on Environment and Development. Since the late 1980s, the theory and practice of sustainable development has been in the focus of attention of scientists and politicians both in Russia and abroad. However, there is no single interpretation of sustainable development. The most correct, in my opinion, is the following definition of sustainable development - it is a continuous process of meeting the needs of present and future generations. The beginning of Russia's transition to sustainable development was laid by the Decree of the President of the Russian Federation "On the concept of the transition of the Russian Federation to sustainable development" in 1996.

According to most researchers, it is the regions that should become the main “arena” for introducing the theory of sustainable development into practice, since they:

act as the most manageable structure, occupying an equidistant position in the administrative space of the country (center - federal districts - regions - municipalities (districts) - citizen);
are historically the most stable territorial entities;
comparable in size to most countries in the world;
acquired during the reform period the experience of combining the practice of stimulating market transformations in their territories with the policy of state regulation of these processes.

So, socio-economic system (region)- this is an integral set of interconnected and interacting social and economic institutions (subjects) and relations regarding the distribution and consumption of tangible and intangible resources, production, distribution, exchange and consumption of goods and services.

Currently, there are several dozen definitions regarding the sustainability of socio-economic systems, and their number continues to grow. This indicates both the complexity of the concept itself and the complexity of the object of study. In some cases, the object of study is the national economy (macroeconomics), in others - the regional economy (mesoeconomics), in the third - the economy of business entities (microeconomics), in the fourth - subsystems of the economy of one level or another. A critical analysis of the existing definitions of the stability of socio-economic systems has shown that a generally accepted concept has not been developed by modern science. At least four distinct approaches can be identified.

Definition	Ator
Resilience as the security, stability, reliability, integrity and strength of a system
The stability of the national economy is determined based on the criterion its security, stability, ability for constant renewal and self-improvement	L.I. Abalkin
Sustainability acts as a guarantor of the integrity of the country and is inextricably linked with the reliability of the state's monetary system	A. Livshits
Sustainability is understood as such a state of the elements of any economic, ecological or other system, when their initial states with a high degree of reliability determine their future states.	A.L. Bobrov
The stability of the economic system in the general sense is the property of this system to maintain its integrity and stability. relative to a given vector of development in the long term in a changing environment	T.M. hemp plant
The stability of the country's national economy as a single system means the strength and reliability of its elements, economic and organizational ties between them, the ability to withstand internal and external loads.	D.V. Gordienko
Stability as relative immutability of the system
Economic sustainability is the ability of the system to maintain and reproduce (restore) the original (or close to it) state in the process internal and external influences on it	A.G. Shelomentsev V.D. Kalashnikov
Sustainability as one of the main dynamic characteristics of an economic system, revealing the property of the system to return to the equilibrium, initial or close to it steady state after any internal or external influence	CM. Ilyasov
Economic sustainability is considered as a permanent, strong position of the system, provided with effective mechanisms of self-regulation and self-development.	T.G. Krasnova
The stability of territorial systems is defined as the relative invariance of the main parameters of the territorial social economic system, its ability to keep them within the given limits under deviating influences from outside and inside	A.L. Gaponenko
System stability is the ability to remain relatively unchanged over a period of time despite internal and external indignation	N.F. Reimers
Resilience is “a necessary condition under which the system must return to a state of equilibrium after any small shock”	M. Blaug
Stability - the ability of a system to return to its original state after an impact on it from the outside	O.V. Kolomiichenko V.E. Rokhchin
Sustainability as the ability of a socio-economic system to maintain a dynamic balance
Stability is “an integrated property of the system to maintain dynamic balance when the parameters of the external and internal environment"	N.V. Chaikovskaya
The economic stability of the economic system of the region is an integrated property of the system to maintain dynamic balance when the parameters of the external and internal environment change within acceptable limits	V.A. Cretinin E.S. Bodryashov
Sustainability as the ability of a system to evolve
The sustainability of the socio-economic system is the ability to effectively use, autonomously modify the resources of its development, continuously increase the indicators of its positive change without increasing or minimizing the costs of basic, non-renewable resources	B.K. Esekin Sh. Sapargali
The stability of economic systems (including regional ones) is understood as the ability to relatively quickly return to the original state or reach a new, higher point on the development trajectory	M.Yu. Kalinchikov
Stability is the ability of a system to function in states close to equilibrium, under conditions of constant external and internal disturbances.	L.L. Terekhov
Sustainability is considered as the ability of a system to function stably in a certain mode of activity.	A.I. Druzhinin HE. dunaev
The stability of the regional economy is its ability to consistently perform developmental functions under the deviating influence of internal and external factors and at the same time ensure an acceptable quality and efficiency of results.	A.M. Ozina
System stability is the ability of a dynamic system to keep moving along the intended trajectory (to maintain the intended mode functioning), despite the perturbations affecting it	L.I. Lopatnikov
The stability of the country's economy is its ability to simultaneously solve the problems of stabilization and development	J. Kornai
The sustainability of the economic system is “a system of economic relations that ensures the long-term development of the economic system with the presence of self-regulation mechanisms (stabilization and balance) that can achieve a comprehensive solution to economic, social and environmental problems in the context of the globalization of the world economy	E.V. Makarova

At the same time, under sustainable development of the regional socio-economic system, we will understand its ability to function stably and develop in the long term in a rapidly changing internal and external environment, achieving the goal of the socio-economic development of the region, namely, ensuring positive dynamics of the level and quality of life of the population on the basis of sustainable and balanced reproduction social, economic, resource and economic potentials.

The question of the stability of systems has worried the minds of scientists for a long time. True, this was due not to economic problems, but to the functioning of the World system, the question of the stability of which was decided before the discovery of the law of universal gravitation. a priori. First, an assumption was made about the fundamental property of the world - stability and chaos, then a system was created. Let us trace some evolution of views on the problem of sustainability, especially since, in our opinion, this is related to the sustainability of socio-economic systems.

Newton was the first to build a dynamic model of the stability of the solar system and immediately ran into the question of its functioning. The scientist got out of the difficulty with the help of the "Great Clockmaker", who from time to time must return the planets to their orbits.

In the future, the concept of stability developed in parallel with the study of planetary motion. In particular, Lagrange considered motion to be stable if it occurs in a closed region of space. In 1773, Laplace formulated a theorem on the stability of the solar system: if the planets move in one direction, their masses are of the same order, the eccentricities and inclinations are small, and the major semiaxes experience only small deviations relative to the mean position, then the eccentricities and inclinations of the orbits will remain small in considered interval. However, it turned out that the theorem is not applicable for large time intervals and for different masses of planets, which is present in the real world. This is also observed in the development of socio-economic systems, where there are no structures of the same size, equal conditions for all organizations, but there is a desire to ensure the effective functioning of the organization for a long period.

Science owes the creation of a mathematically rigorous and consistent theory of the stability of motion to A. Poincaré and the Russian mathematician A. Lyapunov, who owns the most successful definition of the concept of stability: it is not enough to deviate from it over the entire time interval of interest. If there is at least one (!) Movement, at the initial moment, little different from the one under study, which gradually, albeit after a long period of time, noticeably deviates from it, then the movement under study is unstable. When talking about the stability of the solar system, as a rule, they mean the stability of the movement of large planets on an infinite or very large time interval comparable to its age, i.e. system stability occurs when no fundamental changes occur. In this case, the extreme manifestations of instability are leaving the solar system, falling into the Sun, or colliding with another planet. Such an event can significantly change the structure and dynamics of the solar system. It is not surprising that many scientists understand the stability of a system to be precisely the invariance of its elements and the environment. For example, the Soviet mathematicians L. N. Kolmogorov and V. I. Arnold and the American mathematician Yu. Moser developed a theory called the KAM theory. Its application to the solar system gives the following theorem: if the masses of the planets are small enough, the eccentricities and inclinations of the orbits are small, then for most initial conditions (excluding resonant and close to them)(highlighted by us. - Primel. auth.) the movements will be conditionally periodic, the eccentricities and inclinations will remain small, and the semi-major axes will forever oscillate around their original values. But such stability is possible only in the absence of resonances, which cannot be even in excessively large systems. What, then, is sustainability in the face of constant change? After all, if we take as an object of study the socio-economic system, where the functioning of the elements currently occurs with infinite change at the micro and macro levels, then the above theorem rejects the stability of the economy by definition! In fact, there are quite a few types of stability: with respect to perturbations of the initial data (Lyapunov stability), with respect to permanent perturbations, structural, practical, orbital, Poincaré stability, Zhukovsky stability, Lagrange stability, etc. In these definitions lies the possibility to designate the stability of the system in the cases of the presence of perturbations both inside the system and outside it. It is no coincidence that two types of stability are most often used - with respect to perturbations of the initial data and with respect to permanent perturbations (sufficiently small external influences). Stability with respect to perturbation of the initial data is nothing else, as a continuous dependence of solutions on the initial data, fair on an infinite time interval. This dependence can be mathematically represented as follows:

Where L- const Lipschitz; t- time included in time span , where solutions are considered.

The resulting estimate indicates the continuous dependence of the solutions on the initial data. This estimate shows that if the initial points * 10 and * 20 are close, i.e. small value 8 = || * 10 - * 2 o ||, then solutions *, ( t) and 2

(t) will also be close, but only on some finite time interval О t On this segment (1.1) will take the form:

If we want the distance between solutions X,(?) And x 2 (t) did not exceed the given value p on the segment 0 t Г, then we get

The meaning of stability with respect to permanent perturbations is that any solution indignant systems close to elementary moment to the given solution of the unperturbed system remains close to it Always, if permanent perturbations are sufficient small. Stability under constantly acting perturbations is precisely connected with finding out what happens on an infinite time interval with the solutions of the original and perturbed systems, leaving at the initial moment from the same point. Stability with respect to constantly acting perturbations is nothing else, as a continuous dependence of solutions on the right side of the equation on an infinite time interval ( . This is also indicated by the formula below:

The development of real systems is non-monotonous and includes not only progressive directions, but also paths of degradation (which can be replaced by progress, or can lead to collapse), and directions of destruction. In the process of development, which consists of cyclically repeating stages of evolution and a jump, the system is constantly moving from a stable state to an unstable one and back. For a long time it was believed that unstable movements are useless, unobservable, that they must disappear sooner or later, and there is practically no particular use from them. In theoretical terms, this may be so. However, in practice, unstable movements can have every right to exist and be used in practice. Here we enter the area practical sustainability. Analysis of the concept of practical sustainability includes the following aspects:

1) analysis of practically admissible initial perturbations;
2) analysis of practically admissible subsequent deviations;
3) estimation of the time interval beyond which the evolution of the system is of no interest;
4) analysis of the maximum allowable external influences.

If the perturbed solution under admissible initial perturbations (or admissible external perturbations) on given time interval deviates from the unperturbed solution within acceptable limits, then this

the unperturbed solution is called practically stable. We share the statement of A. Filatov: “The Universe, apparently, is theoretically unstable. Perhaps the development goes from bifurcation to bifurcation, and between them the system is practically stable. If this is so, then there is no theoretical stability in nature in principle, and in fact, only instability and its real embodiment - practical stability should be studied.

Let the set В 0 of admissible perturbations of the initial data and the set Bt admissible subsequent deviations of the perturbed solution from the unperturbed one. In many cases, as a set At 0 takes a set of the form:

and as a set Bt a bunch of

An unperturbed solution φ(?) is called practically stable if there exists such a set in the space of admissible parameter values that the solutions y(t), starting in the set B 0 remain in the set IN, on the interval [? 0; ? 0 + L- This is clearly shown in Fig. 1.1.

Rice. 1.1.

We can draw an intermediate conclusion: by identifying a sufficiently large number of types of stability, we are trying to find an answer to the question: how can the system maintain its quality in the presence of perturbations? In our opinion, the answer is as follows: only as a result of constant changes (instabilities) through adaptation, it is possible to achieve the practical stability of the system.

If we continue to describe the functioning of the solar system as an example, we can say the following: in the presence of resonances, the evolution of a dynamical system can go in two ways:

1) the system will go through resonance, which will lead to a sharp abrupt change in the elements of the orbit, for example, its inclination;
2) the system will get stuck in resonance and will pass into a new state with a libration mode of motion, in which the positional elements (major axis, inclination) together or separately will experience fluctuations sometimes of a rather large amplitude.

Any of these scenarios could result in an object moving into a new orbit. And this is the main thing: the object will retain its quality and will develop, albeit in new conditions. Therefore, it can be stated with a certain degree of certainty that the stability of a system is its ability to constantly change, the ability of a system to keep its parameters in a certain range of values, allowing it to maintain qualitative certainty, including the composition, connections and behavior (but not equilibrium!). Such stability is formed in the process of adapting the system to the external and internal conditions that have changed as a result of the catastrophe and is maintained during most of the evolutionary stage.

For the first time, the sustainability of the enterprise began to be considered in the 20s. 20th century It has been argued that when operating with minimal deviations of the system from the standards at its input and output (or within given deviations), it is said to be stable.

An analysis of the economic literature shows that researchers have an almost unanimous opinion regarding the sustainability of an enterprise, although with different interpretations:

- the state of stability is associated with a state of equilibrium, stability, balance, any deviations from equilibrium mean a decrease in stability (or its loss);
- a prerequisite for the sustainability of the enterprise is development;
- the stability of an organization is understood as the preservation of its relative integrity, structuredness and profitability, ensuring the reproduction of the workforce with all possible changes in the environment, as well as preventing the destruction of the structure during crisis phenomena.

As we can see, the definitions include the concepts of balance and development. But there is some contradiction here. In the economic encyclopedia, equilibrium is defined as the state of the economic system, characterized by the presence of balance, balancing multidirectional factors. Equilibrium can be unstable - short-term and stable - long-term. A. Borisov defines the economic balance of an enterprise as the optimal ratio in the production, exchange, distribution and consumption of resources necessary for the existence and development of an enterprise. However, it should be noted here that there are different points of view on equilibrium. In particular, S. Braginsky and J. Pevzner understand equilibrium as such a situation in which, given the invariance of external conditions and parameters, none of the participants in the economic process has an incentive to change their economic behavior.

The semantic meaning of the term "equal-" implies either the equality of any parts, indicators, characteristics of the enterprise or their optimal ratio. Equality, by definition, cannot reflect the dynamic nature of the existence of any system; it is contrary to development, which is associated with excess, addition, change, etc. The duration of equilibrium cannot be a measure of its stability, since maintaining equality does not mean maintaining stability, in some cases it even contradicts the growth or other directions of development of an enterprise, the achievement of which in unstable, difficult to predict conditions is possible only with constant variability in the system’s activity in order to “grope for » the right path of development. This circumstance can be illustrated by the following example: a tightrope walker in a circus is stable when he balances with all parts of the body, even invisible to the viewer.

The optimal combination and ratio of any indicators of the object is a variable criterion, depending on the specific situation, and, therefore, cannot serve as a measure of the stability of the enterprise. More reasonable and consistent with the systematic approach is to consider the enterprise not as an equilibrium system, but as a system of economic relations, the structure of which is formed and changed in accordance with the specific conditions of the enterprise, which determines the balance and sustainability of its existence and development. For example, R. Garipov and M. Khannanov understand economic sustainability as a system of economic relations regarding the formation and use of financial resources, within which an enterprise overcomes objective external restrictions through internal restructuring and adaptation (and in some cases through active opposition), gaining the opportunity to carry out extended reproduction. A large group of authors argue that sustainability is “the ability of a system to carry out normal reproduction of the existing structure of economic relations. The possibility of achieving economic stability and the actual state of the economic system determines the balance of forces and the degree of realization of the economic interests of the subject, on which the preservation of the integrity of the system depends. This approach also takes into account development as the main condition for the existence of an enterprise, the influence of external and internal factors. But what is development? Development is associated with qualitative changes. In other words, change and development are varieties of the process of change, distinguished depending on the level of orderliness of this process. If we consider the object of development as a system, then qualitative changes should be understood as the emergence of new stable structural components - elements, connections, dependencies, i.e. the process of development is associated with the transformation of the structure of the system. Here I would like to draw attention to some methodological points.

Many systems have the property of development, and management systems are no exception. Development is the path that each specific system goes through from the moment of its inception. Development, as you know, is a natural, qualitative change and is characterized by irreversibility and direction. Like any system, the organization management system in its development goes through a number of successive stages, i.e. has its own life cycle: 1) occurrence; 2) formation; 3) maturity; 4) transformation.

The emergence and formation represent a progressive change in the system, since this is the process of formation, organization of the management system. In turn, the transformation reflects the process of disorganization of the management system. The maturity period reflects the stationary state of the system, the realization of its potential. "The stationarity of the system is apparently equivalent to the stationarity of the structure" . During this period, the process of organization is balanced by an equal in strength, but opposite in direction, process of disorganization.

Emergence means the emergence of a new quality. But not a single new management system arises from scratch, even if the emergence of a system is associated with a revolutionary socio-economic transformation, it is still carried out on the basis of the previous system. Having arisen on the basis of old managerial relations, the management system has systemic qualities that are strengthened and expanded in the process of functioning and development. Gradually, the new control system is being “finished”, i.e. forms new subsystems that are necessary to implement their own functions and achieve their goals. “In the process of the development of a phenomenon, the following regularity is usually observed: development proceeds at first not at the expense of all elements, but at the expense of a more or less narrow group of defining elements, followed by the further development of all other elements of the phenomenon.”

Any socio-economic system has historical continuity. As A. Averyanov notes, the process of emergence can be divided into two stages: “1) hidden, when new elements appear in the depths of the old, their quantitative growth takes place; 2) explicit, when new elements form a new structure, i.e. quality" .

The emergence of any new evidence that the old in these conditions has exhausted itself, has ceased to meet the needs of the subject of management. This means that any organizational restructuring of the elements of the system does not lead to improvement, but to its transformation.

The emergence and development of a system is the emergence and development of its contradictions. Becoming is a contradictory unity of the processes of differentiation and integration: the differentiation of elements enhances their integration, and integration, in turn, creates the preconditions for differentiation. As V. Svidersky writes, “... a characteristic feature of development as a complication is the unity of the processes of increasing the diversity of structural dependencies, on the one hand, and the integrity of elements within a given structure, on the other.” This differentiation-integration process is an organizational process: "... the process of complication of the structure can be characterized as a process of differentiation and integration" .

A mature system is in a stable state, but this does not mean that the process of interaction of the contradictory sides of this system has stopped, which causes further transformation. As the management system develops, its functions develop. The system specializes and begins to adapt to a certain way of interacting with the external environment. In the period of maturity, differentiation processes stop - a stable connection is formed between the elements of the system, structuring is completed. Like any other system, the control system can function successfully in the environment in which it was formed. The transition of the system to another environment will inevitably cause its transformation. This is the law of existence of any systems.

But even functioning in favorable external conditions does not exclude the aggravation of internal contradictions that lead it out of a state of equilibrium. The control system is entering the final stage of its development - the stage of transformation.

The transformation of the management system means its transition to a new quality. The reason for the transformation is the contradiction between the form of connection of the elements of the system and their interaction with the external environment. The external environment affects the control system in such a way that it changes the way they interact with the environment. As V. Prokhorenko writes: "... a change in the internal structure of a thing is accompanied by a corresponding transformation of the totality of its external properties, and a certain (essential or insignificant) shift in the internal structure of a given body corresponds to any change in the external world."

Since the functions of individual subsystems and elements change, their connections with the rest of the control system, which still function, also change. There is a decrease in the number of old elements and interactions, an increase in the number of new ones - one system, thus, is destroyed, and another arises. The process of transformation of one control system means the simultaneous process of the emergence of a new one.

Development is associated with a certain direction of the process. Progressive development is characterized by an increase in the level of organization of the system and its complication. The main thing in the direction of development is the emergence of new opportunities in the implementation of the main goals of the system: internal and external requirements.

The organization is an open system, i.e. a system that constantly strives to maintain a balance between internal capabilities and external forces of the environment (i.e., self-stabilizing) to maintain its stable state.

Stability - the ability of a system to approach an equilibrium state under the influence of internal and external disturbances through constant changes. Moreover, we believe that an enterprise always strives for sustainability, not only with minor deviations, as some authors believe. For example, A. Romantsov writes that "the stability of an industrial enterprise is the ability of a management system to ensure the functioning of an enterprise under the influence of external and internal factors in a state of equilibrium and return it to this state after minor deviations."

An analysis of the presented points of view allows us to conclude that the vast majority of authors focus on adaptation, on the adaptive nature of the enterprise's behavior under a certain state of the environment. Under the stability of any phenomenon or process is meant the non-susceptibility of its fluctuations and changes; hardness, durability, reliability; constancy, staying in one state; the ability to maintain a given state, despite the action of various forces. For example, M. Khannanov emphasizes that stability is achieved in such a "state of economic and social relations, in which there are no critical threats and the subject's ability to adequately respond to these threats, as soon as they arise" is preserved. But, as we have already written, the external environment today does not allow us to hope for the absence of catastrophic threats and for the possibility of adaptation: threats arise faster than enterprises have time to adapt to them and predict many of them. Modern conditions raise the question of the inefficiency of the adaptive behavior of the enterprise, they are extremely dynamic and difficult to predict, they require the advanced development of the organization.

In his book The Theory of Catastrophes, A. Arnold gives a number of examples when a stable, steady state of a system's functioning is usually destroyed when it collides with an unstable regime (moreover, at the moment of collision, the convergence rate is infinitely high) or due to an increase (infinitely fast) of self-sustaining oscillations. This explains why it is so difficult to deal with a catastrophe when its signs have already become noticeable: the speed of its approach increases indefinitely as one approaches the catastrophe.

Let us give an example from the theory of rearrangements. The mathematical model of the theory of perestroika was created long before the perestroika of the economy in Russia at the end of the 20th century. The problems of perestroika lie in its non-linearity. The generally accepted methods of control, in which the results are proportional to the efforts, do not work here, and it is necessary to develop control actions based on the sometimes paradoxical conclusions of the nonlinear theory. From the point of view of the theory of restructuring, the change of the administrative system of managing the economy to a market one can be represented as follows (Fig. 1.2).

A. Arnold makes the following qualitative conclusions for a nonlinear system that is in a steady state, recognized as bad, on the assumption that there is a more preferable stable state of the system within the visibility range:

1) gradual movement towards a better state immediately leads to deterioration (point A in fig. 1.2). The rate of deterioration with a uniform movement towards a better state increases;

Rice. 1.2.

2) but as we move from a worse state to a better one, the resistance of the system to a change in its state grows;
3) the maximum resistance (point /;) is reached earlier than the worst state (point c), through which you need to go through to achieve a better state. As the resistance maximum passes, the state of the system continues to deteriorate (to point c);
4) when the system approaches the worst state on the path of restructuring, the resistance of the system, starting from a certain moment, decreases (point b). And as soon as the worst state of the system (point c) is passed, the resistance not only disappears completely, but the system begins to be attracted to the best state (the path to the point e)
5) the amount of degradation required to move to a better state is comparable to the final improvement and increases as the system improves. An underdeveloped system can move into it almost without prior deterioration, while a developed system, due to its stability (read - ossification), is not capable of such a gradual, continuous improvement;
6) if the system can be immediately, abruptly, and not continuously, transferred from a bad stable state quickly enough to a good one, then it will continue to evolve by itself towards a good state. Only the intellectual potential of a person can initiate a leap.

The above laws are the objective laws of the functioning of nonlinear systems, which cannot be ignored. The considered simplest qualitative conclusions from the nonlinear theory of rearrangements are very important and at the same time very reliable: they depend little on the details of the functioning of the system.

In this context, a somewhat limited approach to the definition of sustainability is the emphasis on the financial sustainability of the enterprise, since here, but by definition, there can be no disequilibrium 1 . But it is precisely this approach that remains the main one in determining the sustainability of socio-economic systems.

As we have already noted, for the actual preservation of the organization, more significant activities are needed than those of which our organized whole consisted. An increase in activities can give us the environment, which, in turn, makes it necessary to change the internal relationships of the complex, its structure. A. Bogdanov, drawing a parallel between the social and the living, noted that in a living cell, growth processes change molecular bonds, and in society, the development of an organization leads to a change in structure. An enterprise needs to manage its activities, internal, and possibly external parameters in such a way as to ensure not just sustainable functioning, but constantly create additional benefits, anticipating and ahead of future changes in the environment, realize emerging opportunities and reduce threats, while remaining internally and externally stable. Earlier we talked about the mathematical justification of practical stability. In the economic context, the practical stability of an organization depends not only on the number of activities-resistances concentrated in it, but also on the way they are combined, on the nature of their organizational ties, and the type of organizational structure. Even in economic theory, with a certain discussion of the stability of the monetary unit, the main role is assigned to the person: “The stability of the monetary unit, in addition to its commodity content, is also influenced by factors related to the characteristics of the economic and monetary behavior of individuals” . We consider it necessary to dwell on this in more detail.

Any enterprise is a kind of structural formation with systemic properties. The most important feature of the system is that the elements that make up the system form, in interconnection, a single whole with qualitatively new properties. Considering this sign, it should be emphasized that the system is an ordered set of interconnected and interacting elements, naturally forming a single whole, possessing properties that are absent from the elements that form it. The system has integrity, activity, is capable of development and improvement of its organization. In this regard, the system-wide, integral properties of the system are singled out, which characterize its behavior: utility, efficiency, self-organization, safety, stability, manageability, reliability, survivability. V. A. Ostreikovskii presented the interrelationship of the integral properties of complex systems in an interesting way (Fig. 1.3).

Rice. 1.3.

dynamic systems 1

The integral properties of complex systems in the general case are not a simple sum of the properties of the elements included in the system. For realistic estimates of the state of the system, it is necessary to study all its properties. Any system must correspond to its environment, adapt to it, which makes it possible to speak of a stable organized system, i.e. identify positive and negative changes.

In this context, sustainability can be viewed from two perspectives. On the one hand, sustainability can be understood as preservation, an unchanged state in relation to the disturbing influences of the external and internal environment of the organization, on the other hand, it can be considered as a process, a kind of “forward” movement, which results in the development and improvement of organizational structures and systems. .

In our opinion, the second is more obvious, since nothing is permanent, which means that in any organized system there are always elements of chaos that require coordination. Considering the stability of the monetary unit as an example, it is appropriate to recall the theory of agreements (conventions) - one of the areas of institutional theory within its French school, where an agreement is a certain form of coordination of the interaction of individuals, developed under the influence of the entire set of formal and informal norms and rules of social behavior . Individuals act in various forms of coordination or agreement regarding the observance of norms of social behavior, i.e. operate "in an environment consisting of many heterogeneous spheres or worlds" . In tektology, the organization is an "organizational complex", the elements of which are various activities-resistances that are in a certain combination and interaction. Moreover, this relationship is quite flexible and mobile, it contributes to an easy rearrangement of elements; it is no coincidence that this nature of connections has been called "organizational plasticity". Organizational plasticity helps to increase the adaptability of the complex to new changing environmental conditions, which favors the sustainable development of the system. However, a plastic organization is fraught with one contradiction: the mobility of the elements of the system allows the destruction of the links between them, which causes an imbalance and leads to a kind of instability of the organization. Thus, organizational plasticity, on the one hand, leads to a complication of organizational forms, an increase in their adaptability, organization and flexibility, on the other hand, to a decrease in strength, stability, and the emergence of new “vulnerabilities”.

Being in constant interaction with the environment, the system gives up its activities, but at the same time takes the same amount from the environment. Essentially, the system is evolving. In our opinion, development is a way of existence of a complex in a changing environment.

Processes arise inside the system aimed at overcoming external influences and restoring balance. Thus, the preservation of the forms and stability of the entire system is possible only through progressive development, otherwise it simply will not survive under the influence of an increasingly complex environment.

Based on the existence of relationships and interactions between systems, i.e. on the existence of a coordinated development of systems, it can be argued that the stability of the organization depends on the level of organization of the system. The stability of the entire system is facilitated by the fact that one part of the system assimilates what is rejected by the other. In addition, the stability of the complex can be ensured through additional connections with other systems and an increase in the diversity of the dino system. The more diverse the system, the greater the chance that one of its destroyed elements can be replaced by another. “Nature, for all its infinity and eternity, has a beginning and an end ... Stability is the desire for balance, the interaction of beginning and end.” In other words, the normal state of the system is the non-equilibrium state. There are objective reasons for this, which we have already stated when speaking about a person, about the diversity of his states.

Continuing the conversation, we want to draw attention to the approach of K. Waltukh, who proceeds from the fact that in the process of production activity a person “systematically creates from objects found in nature such products that either are not generated at all by spontaneous natural shaping, or are generated only relatively rare." According to K. Waltukh, production is the production of information. Information, as a measure of diversity, creates uncertainty, relative disequilibrium, which contributes to stability. Information interaction by its nature is a resonant interaction. In mentioning the stability of the solar system, we emphasized the role of resonances in achieving stability. In this regard, this is how L. Amirkhanova defines the stability of the economic system: “The stability of economic systems is the ability to receive and process information in a timely manner, form resources and produce products with the required performance in accordance with consumer demand under the influence of disturbing factors of the internal and external environment” .

To preserve the system in a changing environment, a simple exchange equilibrium is not enough. Only an increase in the sum of activities can serve as a guarantee of stability, when new adverse effects meet not with the former, but with increased resistance. And the destruction of the system occurs precisely because of the decrease in the sum of these activities-resistances.

If the organization develops, then this leads to a further complication of the organization, the emergence of additional connections that lead to more stable structural relationships.

In cybernetics, stability characterizes the ability of a system to function in states at least close to equilibrium under constant external and internal disturbances. Equilibrium is defined as dynamic, i.e. it is not so much a state as a process characterized by some equilibrium trajectory of the system. In this case, the trajectory will be equilibrium if it steadily and in the shortest way in time or space leads the system to the goal. Achieving a precisely defined state of equilibrium and staying in this state for long periods of time is rather an exception, a limit that can only be approached. Although approaching such a limiting state requires many qualities from the system, which in combination are defined as stability.

In reality, there are not absolutely, but relatively stable states of the organization. Such states are not states of complete equilibrium, but are similar to equilibrium. In such a “quasi-equilibrium” state, there is a relatively weak exchange of energy between the system and the environment, but a relatively large information connection between them.

The greater the heterogeneity of internal links in the system, the less stable it is, and, conversely, with an increase in their homogeneity, the stability of the system increases. In the first case, the existing structural contradictions are preserved and more and more new ones are added to them, in the second, the ongoing destruction tears away from the complex, first of all, the least firmly connected with it elements, breaks the most contradictory ties. The complication of these connections, the growth of their heterogeneity reduce the harmony and stability of the entire system. And sooner or later, the development of the system leads to instability and crisis, as the parts of the whole become different, and the accumulated systemic contradictions outweigh the strength of additional connections between the parts and lead to their break, to a general disruption of organizational unity.

The stability of the structure depends on: 1) the presence of mechanisms designed to ensure that some of the most important characteristics of the system remain practically unchanged regardless of all kinds of external influences; 2) the presence of the so-called structural redundancy, i.e. the possibility of duplication of essential elements of the system. Such redundancy allows not to disrupt the functioning of the system under adverse external influences, and therefore to maintain the stability of the structure. However, there is a limit to such preservation. If the conditions of the external environment go beyond the boundaries in which the system with the given structure functions stably, then at first there is a violation of the basic functions, and then the structure as a whole. To prevent such a situation, systems can compensate for unfavorable disturbances due to a greater number of their varieties, the presence of wider boundaries of changes in each disturbance, and efficiency over time. Essentially, the stability of the system is a consequence of the resolution of the crisis.

The crisis of any system is a transition from one stage of development to another, from one qualitative state to another with its own critical point. The cause of any crisis is the destruction of some internal connection, leading to the loss of stability of the equilibrium in which the system was located.