RESEARCHING THE EFFECTS OF COMPLEX SYSTEMS THEORY IN ECONOMICS

Abstract

Complex realities define our daily lives: complex processes work in nature, and complex structures defne our social environment. Complexity is inherent in decision-making and connected behaviors; complexity issues revolve around technologies; complexity is embedded in different policies. The nature of complexity also applies to how the world economy system works, as it consists of complex actions and interactions between individual institutions, national and international companies, entire societies, and the policies that govern them. Complexity economics is no addition to the standard economy, nor does it consist of adding agent-based behavior to standard models. It is a different way of seeing the economy - the perception of the economy not as a system in balance but as one in motion, which is "calculated" constantly, always building again. Where the economy of equilibrium emphasizes order, determination, deduction, and stasis, this new framework emphasizes contingency, indeterminacy, meaning, and openness to change. There is another way of saying this. Until now, economics has been a science-based on nouns rather than verbs.

Headnote

Abstract: Complex realities define our daily lives: complex processes work in nature, and complex structures defne our social environment. Complexity is inherent in decision-making and connected behaviors; complexity issues revolve around technologies; complexity is embedded in different policies. The nature of complexity also applies to how the world economy system works, as it consists of complex actions and interactions between individual institutions, national and international companies, entire societies, and the policies that govern them.

Complexity economics is no addition to the standard economy, nor does it consist of adding agent-based behavior to standard models. It is a different way of seeing the economy - the perception of the economy not as a system in balance but as one in motion, which is "calculated" constantly, always building again. Where the economy of equilibrium emphasizes order, determination, deduction, and stasis, this new framework emphasizes contingency, indeterminacy, meaning, and openness to change. There is another way of saying this. Until now, economics has been a science-based on nouns rather than verbs.

Keywords: Complex Systems Theory, entropy, self-organization, butterfly effect, disorder, nonlinear dynamics

Introduction

The notion of a system comes from the Greek word "system," which means "whole" in translation. Therefore, by the concept of a system, a whole is understood.

Everyone around us - atoms and galaxies, molecules and living organisms, the universe and society - is made up of systems. At the same time, the systems research represents the research mysterious research character of the world, of the determination of the legitimacy of the development of nature and human society.

After long and contradictory searches, the science of the twentieth century synthesized the scientific category of system. It gave the possibility to both theory and practice to go beyond the simplistic understanding of reality and direct man to rethink organizing and carrying out his social, economic, political activity.

Systems theory is a relatively young science, which is at the junction of many fundamental and applied sciences. This is a kind of biology of mathematics, the field of study of different systems' behavior.

Complex Systems Theory is the set of knowledge, which results from studying the existence of interrelationships, from revealing the types of relationships specific to phenomena to deciphering functions, dysfunctions, and the ends of some processes.

Complex nature of the system

Complexity is a ubiquitous feature of the contemporary world. When we say that the world is interconnected, we implicitly say that it is complex. The best way to explain this concept is through the complexity of Kolmogorov.

Kolmogorov complexity is a modern notion of randomness that deals with the amount of information in individual objects: point randomization rather than mean. Andrei Kolmogorov proposed it in 1965 to quantify the information and eventuality of individual objects in an objective and absolute way.1 For example, the Kolmogorov complexity of a string demonstrates that it cannot be more than a few bytes longer than the length of the string itself. So, for example, we have two strings of the same number of characters:

acacacacacacacacacacacacacacacacacacac, and 6cij5i2pocv4wix8rx2y39uegc5q85s7

The first string has a short description, namely "write ac 16 times", composed of 17 characters. However, to describe the second string, we need to write 38 characters "write 6c1j5i2pocv4w1x8rx2y39uegc5q85s7". Therefore, we can see that writing the first string has "less complexity" than writing the second. Finally, the issue of using the notion of a complex in this new science of complexity is related to the ambiguity that this word can induce through the significant differences in meaning associated.

According to the theory of complex systems, a system is the totality of interdependent elements. The components of the system are called its elements until they have a relationship with this system. The interconnection of the elements of the system determines its integrity. If an element of the system loses its connection with the system, it turns into a new system, just like the other part of the system, which turns into another new system, so all systems have their elements. Analogously, all social systems are composed of elements.

Complex systems are characterized by some properties: simple rules of complex behavior; butterfly effect of deterministic chaos; emergency.

The identification and classification of systems, the correct determination of their nature is possible only by applying a measuring instrument (evaluation). Such an instrument, in our situation, can be space and time.

For systems research, as a basis, the internal space of the system and its own time are taken. These two parameters of the real world manifest themselves more general. On the one hand, they include all forms of systems, and in any combination, and on the other hand, they reflect all the diversity of systems and their most little differentiation. Social systems, like other systems known in nature, are measured by these parameters.

To capture the essence of complexity, one cannot use the study model of classical science, which involves the fragmentation of the whole and thus the study of isolated parts. Complexity is created from simplicity, results from the theory of complex systems, and demonstrates the connection of the parts with the whole. The set of naturally interconnected elements represents a particular integral formation, a unit. The system can be seen as an order due to the planned and correct arrangement of the components in a certain connection. On the other hand, the system acts concerning the environment. The system is a set of interconnected elements, united by functional integrity, unity of purpose, and, at the same time, the ownership of the system itself is not reduced to the sum of the properties of the elements.

The reality is that complex system is everywhere, as evidenced by the science of complexity. The American researcher Kevin Dooley highlights, in his publications, the basic principles of the complex system, namely: (I) order and control in such systems are emergent properties and not predetermined; (II) their history is irreversible, (III) the future in these systems is uncertain.2

At the same time, any complex system is characterized by a chaotic state. The chaotic state is characterized by uncertainty, probability, and chance, which fall within the limits of the concept of cybernetics and entropy (if information in the system is the measure of system organization, then entropy is the measure of disorganization; in fact, it can quantify the insufficiency of information in the system).

James Clerk Maxwell described the law of entropy (the second law of thermodynamics) as follows: "If you throw a glass of water into the sea, then fill it again, you will not get the same water." This law is much discussed and is one of the fundamental laws, which produces considerable effects in the most fundamental science - physics. Many scientists were working on the formulation and discovery of this law in the nineteenth century - Sadi Carnot, Lord Kelvin, Josiah Gibbs, and Rudolf Clausius. Among these scientists, probably the most significant contribution was made by the founder of statistical mechanics, Ludwig Boltzmann, due to his intuition about the role of entropy in nature.

Without an impact from the outside, in nature, everything tends to a state of equilibrium. Then, in 1824, the French physicist and military engineer Sadi Carnot considered the "father of thermodynamics," drew attention to this.

The current form of the second law uses, rather entropy than the caloric, which Sadi Carnot used to describe the law in his work "Reflections on the motor power of fire".3 The caloric refers to heat, and Sadi Carnot realized that a specific caloric is always lost in the movement cycle. Thus, the concept of thermodynamic reversibility proved wrong, proving that irreversibility is the result of every system that involves work. As for the concept, the entropy (in Greek cycle) determines the system's state from internal order. The higher the order, the lower the entropy.

William Thompson, also known as Lord Kelvin, formulate Kelvin's statement, which says that it is impossible to turn heat entirely into a cyclical process. This means that there is no way to convert all the energy of a system into work without losing energy. In 1851, Lord Kelvin specified Rudolf Clausius' principle through formulating "the world's entropy tends to the maximum." Because, in an isolated system, the maximum entropy is reached in a state of equilibrium, then, from Clausius' formulation, it results that the Universe has a beginning and will end when all processes cease, and the state of equilibrium will be installed.4 According to classical thermodynamics, the retention of entropy growth is possible only by reversible processes, from which it follows that entropy is an indicator of irreversibility (until Clausius, only reversible systems were examined). Destroying order is an irreversible process and, without outside involvement, the order cannot be created; therefore, the reduction of entropy can only be achieved by applying an effort.

At present, it is known that increasing entropy cannot be reduced by amplification of the disorder because the order at the macro-level coexists with the chaos at the micro-level. Thus, the order is closely linked to disorder - one implies another.5

Last years of the nineteenth century, many physicists found themselves discussing the validity of the mechanical view of the world, which had been taken as such until then. The question at the heart of the debate was whether Newtonian mechanics, honored over time, could still be considered a valid description of the whole of nature.

Max Planck was deeply interested (even obsessed) with the second law of thermodynamics. According to this law (in one of its many versions), no process is possible in which the only result is the transfer of heat from a colder body to a hotter one. However, with the help of the entropy concept, introduced by Rudolf Clausius in 1865, the law can be reformulated to a state that the entropy of an isolated system always increases or remains constant.6

Ludwig Eduard Boltzmann was in the opinion of Max Planck, "the one who deeply understood the meaning of entropy".7

The second law has its roots in the middle of the 19th century in the works of Carnot and Clausius. Carnot discovered the incomplete conversion of heat into work, but it took years for the notion of "entropy," which we owe to Clausius.

Our understanding of the concept of entropy is related to "disorder," although a precise meaning of this concept is rarely given. Boltzmann elucidated the problem of thermal equilibrium through the formula for calculating the diffusion of gas molecules - "Boltzmann distribution" - which became a fundamental element of thermodynamic calculations (also called "Maxwell-Boltzmann distribution").8

Another necessary component to analyze is the gestion of complex systems, which, according to the classical approach, is based on the concept that the result of external action management is a unique, linear, and predictable consequence of the "forces" applied, which corresponds to the following scheme: managed action - a result desired. According to Isaak Newton, all physical actions are determined by both their forces and their causes. The purpose of nature research ("Philosophia Naturalis") is to determine these forces through mathematical laws ("Principia Mathematica") and to explain further and determine all physical events. They were observed in the past and the future. One hundred years later, this idea turns, in the Frenchman Pierre Simon de Laplace, into the belief that it is possible to make the total calculation of nature under ideal conditions when all the laws of force action and the initial conditions are known ("the demon Laplace").9

This assumption is valid for linear dynamical systems, for example, in the case of a harmonic oscillator. An insignificant displacement of the mass fixed on a spring causes insignificant oscillations, while a consistent displacement will generate significant oscillations. The cause and effect in this situation are similar. The mathematical analysis will lead to a linear equation, which can be solved quite easily. In a less sophisticated view, the output of deterministic dynamical systems can, in principle, be accurately predicted.

On the contrary, nonlinear equations do not always allow a very accurate solution. Thus, as an example can serve the problems of some bodies in celestial mechanics, where the problem of determining the gravitational influence of one body on another, in the case of more than two celestial bodies (the so-called problem of three bodies). For the first time, in 1892, Jules Henri Poincare demonstrates that, in the case of the nonlinear problem of several bodies, chaotic, unstable orbits can appear, which, to a large extent, depend on the initial indicators and cannot be calculated in advance.

From Poincare's work, we can distinguish the postulate of chaos theory about dependence on initial conditions. The further development of science, especially quantum mechanics, contradicted Laplace's determinism. In 1927, the German physicist Werner Heisenberg discovered and formulated the principle of uncertainty. This principle explains why certain random phenomena are not subject to Laplace's determinism. Heisenberg demonstrated the principle of uncertainty through the radioactive decay of the nucleus. So, due to the minimal size of the kernel, it is impossible to know all the processes that take place inside it. Therefore, no matter how much information about the kernel we have collected, it is impossible to predict precisely when the kernel will disintegrate.10

Finally, Andrey Kolmogorov (1954), Vladimir Arnold (1963), and Jürgen Moser (1962) prove the well-known theorem: the trajectories in the phase space of classical mechanics are neither totally regular nor totally irregular, but largely depend on the initial conditions.11 Insignificant deviations in the initial data lead to the development of entirely different trajectories ("butterfly effect"). Therefore, it is impossible to calculate, in advance, the future directions of development in a chaotic system, although, mathematically, they can be determined.

Results and Discussion

From the above exposed, we can see that at the level of complex systems - biological, cybernetic, social -, there is no total quantitative equality and qualitative identity between cause and effect, here intervening the element of qualitative transformation and the novelty production.

Although much has been investigated about the nature of complex systems and their dynamics in the last half-century, the dream of a global theory remains elusive; "General Systems Theory" does not seem to have produced a general systems theory. Indeed, many theorists today question that any universal theory is possible. It is said that the many types of systems in nature and human society are so diverse that the commonalities between them are of trivial importance in comparison with their profound differences. However, over the last 50 years, we have gained a much better understanding of how complex systems work.

Yet, there is an apparent lack of a comparable sense of progress in of systems theory towards understanding "why" there are complex systems in nature. Systems science seems to lack a causal theory (or theories) that addresses the issue of accounting for the "progressive" evolution of complexity over time. Some researchers have turned to physics and, more precisely, to non-equilibrium thermodynamics to explain the reason for the existence of complexity in nature. The most notable example of this is Ilya Prigogine's work on the role of energy in producing what he calls "dissipative structures." Prigogine, an echo of Herbert Spencer in the nineteenth century, argues for discovering a "universal law of evolution." However, other theorists are not convinced that physical systems, such as Bénard cells, can be treated similarly to living systems. Some theorists, such as John Holland and Stuart Kauffman, although they do not support Prigogine's energy-centered theory, hope to find other laws of complexity in nature.12 Kauffman believes that only "a few profound and beautiful laws can govern the emergence of life and the population of the biosphere." However, these laws remain to be discovered in the future.13

In this context, one of the most significant theoretical contributions of the twentieth century can be considered the works of Ludwig von Bertalanffy, who inspired the movement of systems science. Ludwig von Bertalanffy was the creator of General Systems Theory (GST), proposed the term, developed it in detail in his many writings, and was a crucial figure in the group that carried it forward and spread the concept. Indeed, the movement of systems would not have taken the form it has without Bertalanffy. He preceded his time, being beyond conventional opinions.

Von Bertalanffy proposed the theory of open systems to explain the phenomena of life. According to him, open systems, living organisms are examples of systems that do not follow the second law of classical thermodynamics and are characterized by negative entropy. This property explains the development of the body, differentiation, and increasing complexity.14 It also explains the objectivity, intent, and complexity of human and animal behaviors. Consequently, von Bertalanffy rejected the reductionism and "atomism" that characterized American behavior and Orthodox psychoanalysis. Instead, he supported the organic and holistic approach and the unique features of human behavior, such as symbolism and value creation. Symbolic and value systems have played a more critical role in human motivation than biological impulses. The influence of von Bertalanffy's theory of general systems went beyond biology, extending to psychology, psychiatry, sociology, cybernetics, economics, and philosophy. Using the general framework of systems theory, von Bertalanffy sought to reconcile the natural scientific approach to human behavior with the humanistic one.

Is the evolution of complexity an unsolved and perhaps can be solved mystery? In science, there is already a general theory of complex living systems (including artificial systems) called the "Synergism Hypothesis," developed in-depth in a book of the same title by Peter Corning. At the same time, it is considered that this paper, published in 1983, was premature and was addressed, first, to evolutionary biologists, anthropologists, and other people in the social sciences, not to those who study systems.15 Thus, the theses proposed by Corning are only now gaining recognition in each of these various scientific communities.

The interests of Peter Coming's research are in bioeconomics, and the hypothesis of synergism, according to him, is a vaguely familiar term for many of us and is, in fact, one of the important principles of organization the natural world. The synergism hypothesis states that synergy is more than a simple category of stimulating and ubiquitous effects because it is also a primary evolving causal agency. Synergistic functional effects of different types are a necessary, if not sufficient, the requirement for the evolution of cooperation and complexity at all levels of biological organization.16

This theory is essentially an "economic" theory of complexity, a functional theory different from gene-centered theories, self-organizing postulates, "laws" of complexity, or even theories of random historical contingencies. Moreover, this theory is eminently testable and lends itself to falsifiable predictions.

Mitchell J. Feigenbaum has discovered that a universal way to transition from order to chaos can take place. Using computer calculations, he demonstrated that the same constant behavior would occur in a comprehensive class of mathematical functions between the sciences before the onset of chaos.17 This number, around 4.6692, came to be known as the Feigenbaum constant. His scientific work has impacted many disciplines, including chemical kinetics, statistical physics, hydrodynamics, meteorology, and economics.

Fractal geometry can also provide a way to understand complexity in "systems," according to Benoit Mandelbrot. Mandelbrot emphasized use fractals as realistic and practical models for describing many "harsh" realworld phenomena.18 He concluded that "real roughness is often fractal and can be measured." The timing and size of earthquakes, the variation of a person's heartbeat, and the disease prevalence are just three cases in which fractal geometry can describe the unpredictable. On the other hand, Mandelbrot saw financial markets as an example of a "wild event," distinguished by concentration and long-term dependence. He tried to apply fractal mathematics to describe the foreign exchange market - in terms of profits and losses made by traders over time and found that this method works well [293].19 Fractal mathematics cannot be used to predict significant events in chaotic systems, but it can tell us that such events will happen.

Another direction in the research of complex systems is focused on social systems. The central concept around which the theory of social systems is built, as Niklas Luhmann later developed it, is the notion of autopoiesis, initially developed by two Chilean biologists, Humberto Maturana and Francisco Varela.20 The fundamental element of the autopoiesis concept is the idea that different system components interact in such a way as to reproduce the system elements. That is, through its elements, the system self-reproduces.

Autopoietic systems are thus systems that reproduce from within: for example, a plant reproduces its cells with its cells. Luhmann argued that the basic idea of autopoiesis could be applied to the biological system and many nonbiological systems. He mastered the original biological concept, modified it, and applied it to the social field. Like biological systems, social systems have been conceptualized as systems that reproduce their elements based on them.21

A significant challenge facing contemporary theory is overcoming its fixation on written narratives and print culture. In this presentation of a general theory of systems, Germany's most prominent and controversial social thinker proposes a contribution to sociology that restores our understanding of meaning and communication.

Luhmann acknowledges that there is no longer a mandatory representation of the society within the society but refuses to describe this situation as a loss of legitimacy or representation crisis. Instead, he proposes that we look for new ways to deal with the forced selectivity that marks any self-description in the conditions of modern, functionally differentiated society. For Luhmann, the end of metanarratives does not mean the end of theory, but a challenge to theory, an invitation to open to theoretical developments in several disciplines that have successfully worked with cybernetic models, which no longer require much the fiction of the external observer.

Another characteristic of living and human systems is selforganization. Even the reverse connection is presented as a relatively simple form of self-organization, allowing different systems to control their activity. Cybernetic systems create both the means of homeostatic maintenance and the resources for their possible development. It can be said that systemic self-organization uses order and disorder in the service of organizational complexity, in the arsenal of systemic structures and restructurings.

Still, the father of the market economy, Adam Smith, in his research, was based on the concept of self-organization of the complex economic system, in which the production and consumption of goods between producer and consumer determine the economic dynamics. To describe this dynamic, Smith analyzed the "natural" price, consisting of the cost of producing the goods. When the market price exceeds the natural price, the profit increases and leads to the production expansion and, thus, to the return of the market to the natural one. The inverse relationship occurs when the market price is lower than the natural price. Thus, through the mechanism of interdependence between the possibilities of increasing profits and the risks of losses, the market economy system is selforganizing and tends towards a state of absolute balance between production and consumption. In this way, Adam Smith proposed conservative self-organization, where the economic balance is achieved through an invisible hand ("invisible hand"), and which leads to a social order in society ("wealth of the nation").22

But the behavior of economic systems does not allow comparison with the conservative self-organization of crystals and rigid bodies near thermal equilibrium. The social sciences are based on social interactions and their implications for society. Usually, the social sciences are neither very quantitative nor predictive nor produce experimentally testable predictions, being, primarily, qualitative, and descriptive. This is because, until recently, there was a considerable shortage of longitudinal and multidimensional data. The situation changed rapidly, with the new tendency of homo sapiens to leave electronic fingerprints in virtually all dimensions of life, and the problem of obsolete data in the social sciences disappears quickly.23 Another fundamental problem in the social sciences, according to Thurner, is the lack of reproducibility or repeatability. Often, certain events take place once in history and are not possible to repeat. As in biology, social processes are difficult to express mathematically because they are evolutionary, out of balance, and context dependent.

Short-term fluctuations in the propensity to consume, the inelastic reaction in the behavior of producers, as well as speculation in commodity markets, can be examples of sensitive reactions in the economic system. The fact that fluctuations, on the one hand, can contribute to great leaps in economic development (for example, the role of such technical innovations as the weaving machine and the steam engine in the industrial revolution) and, on the other hand, cause chaotic behaviors and uncontrolled (stock market crashes, mass pauperism, and unemployment) was demonstrated by the secular historical experience after Adam Smith.

Karl Marx determined the self-organization of the market economy through simple and expanded production schemes. His critical analysis reveals the transition in phase, in which the development of economic systems, saturated by crises and changes in social structures. From the point of view of complex dynamic systems, the Marxist analysis of the phase transition is realistic.

Synergy is often called "the science about the complicated", the teaching of self-organization and the universal laws of the evolution of complex dynamic systems; it is currently considered one of the most popular interdisciplinary approaches in the future. One of the founders of synergy, the German physicist Hermann Haken, determined it not only as the science of self-organization, but also as the theory of "common action of several subsystems, as a result of which a new structure appears at the macroscopic level".24 This theory he proposed to be studied in a new discipline, called synergy by him, whose meaning comes from the Greek word "synergeia", which, in translation, means "common coordinated action". According to Haken, synergy has two meanings: on the one hand, the common action of the elements of the composite system; and on the other hand - the cooperation of scientists from different fields [402].25 At the beginning of the 80s of the last century, the science of self-organization was called, in Germany, Synergy (H. Haken), in French-speaking countries - the theory of dissipative structures (I. Prigogine) and in the USA - the theory of dynamic chaos (M. Feigenbaum). In the literature, these "branches" of the science of self-organization are also called "complex science".

From the point of view of the history of science, according to the German researcher Klaus Mainzer, it is remarkable that the "butterfly effect" in economics is mentioned since 1890 by the English economist Alfred Marshall, around the same time when Poincare establishes the nonlinear character of celestial mechanics. Marshall pointed out that an enterprise that accidentally reaches a high level of commodity production can quickly outperform its competitors if, as production commodity increases, so do production costs.26 Hence the following conclusion: it is important to note in time the parameters of the order, which could have played a dominant role in the dynamics of the systems. In fact, there is a need to develop economic systems for early prevention as in the case of disease prevention or weather forecasting. In both situations, we encounter the nonlinear dynamics of complex systems. Based on the symptoms of the disease or meteorological data, it is possible, through various mathematical methods (analysis of numerical strings; determination of attractors in the phase space; Lyapunov exponent), to determine the future development trend. In the process of researching social systems, the multidimensionality of these systems must be considered. Mathematically, the social sciences are more complicated than the natural sciences because the models used are more difficult. But the qualitative perception of using nonlinear dynamics models is quite useful and insures us against unexpected events.

As an open system, which is in a permanent process of exchange of substance, energy and information, the market economy system cannot tend towards a state of equilibrium between "natural" and market prices. By analogy with biological ecosystems, the market economy undergoes permanent changes and reacts, sensitively, to the smallest changes. These processes are large in scale and involve multi-level interactions. Unfortunately, according to Klaus Mainzer, at present, the tools of social science, including economics, rarely surpass the methods of linear statistics. What is missing so far in the social sciences are the massive joint and coordinated efforts between scientists that have taken place in physics (CERN), biology (the genome project) and climate science. However, two important components have been developed in the social sciences and play a crucial role in the theory of complex systems: multilayer interaction networks and game theory.27

Elements of using nonlinear dynamics models can be observed in the theory of economic development of Joseph Alois Schumpeter.28 The author focused on the so-called "innovative shocks," which we could attribute to "energy supply." These cause synergistic effects of qualitative change of the system: the economy without innovation remains stagnant, and innovative impulses can lead to bifurcations and chaos. Similar meanings can be found in the dynamics of John Maynard Keynes,29 in the monetary approximation of James Tobin,30 in the neoclassical model, and the model of "self-organization" of Wei-Bin Zang.31 As W.B. Zhang, the synergistic economy studies the properties of evolutionary economic systems, in which "order gives rise to chaos, but in chaos, a new order appears." The author tries to follow how the endogenous appearance of chaos is possible in the evolutionary process following the dynamic interaction of different forces. In his view, chaos characterizes such economic systems as labor, financial markets, urban, transportation, and communications.

Another researcher, Constantin Valituh, in the theory of informational value, develops the concept according to which, in the post-industrial (informational) society, information, knowledge, and their practical ways of application replace work as its source of surplus-value. However, even these models did not contribute to elucidation in describing the temporal links of continuous processes and the behavior of extra-dynamic transformations from order to chaos. In this context, it seems remarkable that, until recently, the network was not considered relevant to the "queen" of the social sciences - the economy, even if networks dominate almost every area of the economy. The general economy has ignored networks (production, distribution, trading and consumption, ownership, information, and finance) in favor of the economy's somewhat unrealistic equilibrium perspective.32

Conclusions

Economic science is constantly changing. In recent decades, it has generated some new approaches.

The traditional framework sees behavior in the economy as in a state of equilibrium. People in the economy face well-defined problems and use perfect deductive reasoning to justify their actions. On the other hand, the complexity framework always perceives the economy as a process on which its ever-changing actions are based. Individuals try to understand the situations they face using any reasoning they have at hand and, together, create results to which they must react individually. The resulting economy is not a well-driven car but a complex evolving system, which is imperfect, constantly rebuilding, and full of vitality.

The use of the complexity approach in economic research is becoming more widespread, as it allows, compared to other earlier approaches, to detect irregular effects existing in economic realities; at the same time, it offers the possibility to understand more deeply the nature of their appearance, to identify and, in a proper way, to influence the course of economic processes. The nature of economic systems, being essentially a complex one, can only be investigated in the context of the theory of complex systems.

Footnote

1A. Kolmogorov, Mathematics in its historical development, Moscow: LKI, 2007.

2K. Dooley, Complexity science models of organizational change. Handbook of Organizational Change and Development. Oxford University Press S. Poole and A. Van De Ven (eds.), 2015, 354-373.

3 S. Carnot, Reflexions sur la puissance motrice du feu. [online]. Paris: Chez bacheliere libraire, 1824. http://www.bibnum.education.fr/sites/default/files/42-camottexte-f.pdf

4 A. Stromberg, P. Semchenko, Physical chemistry. Moscow: High School, 2001.

5 I. Prigogine, The philosophy of instability, Philosophy questions, 1991, No. 6., 46-57.

6 Physicsworld. Max Planck: the reluctant revolutionary. [online]. https://physicsworld.com/a/max-planck-the-reluctant-revolutionary/

7 Financial architecture of the post-crisis world: the effectiveness of solutions. Institute for the Post-Crisis World. [online]. http://www.postcrisisworld.org/research/podrobnee/002/.

8 Ş. Tiţeica, Course in statistical physics and quantum theory, Timisoara: All Educational, 2000.

9 I. Prigogine, I. Stengers, Order from Chaos. A new dialogue between man and nature. Moscow: Progress, 1986.

10 J. Mawhin, Henri Poincare. A life in the service of science. [online]. Poincare Symposium in Brussels, Octobre 8-9, 2004. http://www.ams.org/notices/200509/comm-mawhin.pdf.

11 I. Andrianov, R, Barantsev, L. Manevich, Asymptotic mathematics and synergetics, the path to integral simplicity, Moscow: Editorial URSS, 2004.

12 J.H. Holland, J. Miller, Artificial Adaptive Agents in Economic Theory. American economic association papers and proceedings, 81, 2, 1991, 365-370.

13 S. Kauffman, At home in the universe: the search for the laws of self-organization and complexity, Oxford: Oxford University Press, 1996.

14 L. Von Bertalanffy, General System Theory: Foundations, Development, Applications. New York: Braziller, 2003.

15 P. Corning, The synergism hypothesis: A theory of progressive evolution. New York: McGraw-Hill, 1983.

16 P. Corning, Synergy Goes to War An Evolutionary Theory of Collective Violence. The Celebration of the, 100th Anniversary of Ludwig von Bertalanffy's Birthday, University of Technology, Vienna, Austria, November 1-4, 2001.

17 M. Feigenbaum, Universal behavior in nonlinear systems. Physica D: Nonlinear Phenomena, vol. 7, Issues 1-3, May 1983. pp 16-39.

18 B. Mandelbrot, Fractals and Chaos. The Mandelbrot Set and Beyond. New York: Springer-Verlag, 2004.

19 B. Mandelbrot., R. Hudson, The Misbehavior of Markets: A Fractal View of Financial Turbulence. New York: Basic Books, 2006.

20 H.R. Maturana, F.J. Varela, Autopoiesis and Cognition, Boston Studies in the Philosophy and History of Science, vol. 42, 1980. 4

21 N. Luhmann, Social Systems, Stanford: Stanford University Press, 1995.

22 A. Smith, The Wealth of Nations, Bucharest, Publica, 2011.

23 S. Thurner, R. Hanel, P. Klimek, Introduction to the Theory of Complex Systems. Oxford: Oxford University Press, 2018.

24 G. Haken, Can we apply synergy to the human sciences? Synergetics and Psychology. Social Processes, Issue 2. Moscow, 2000, 12.-16.

25 N. Klimontovich, No synergy formulas, Minsk: Higher School, 1986.

26 K. Mainzer, Thinking in Complexity - The Computational Dynamics of Matter, 5st edition, Berlin: Springer-Verlag, 2007.

27 K. Mainzer, Thinking in Complexity - The Computational Dynamics of Matter, 5st edition. Berlin: Springer-Verlag, 2007.

28 J. Schumpeter, The Theory of Economic Development, Moscow: Directmedia Publishing, 2008.

29 J.A. Tobin, General Equilibrium Approach to Monetary Theory, [online]. Journal of Money, Credit and Banking, Vol. 1, No. 1. Ohio: Ohio State University Press. 1969, 1529. http://www.deu.edu.tr/userweb/yesim.kustepeli/dosyalar/tobin1969.pdf.

30 J. Keynes, General Theory of Employment, Interest and Money, Bucharest: Publica, 2009.

31 V. Zang, Synergetic Economy. Time and changes in nonlinear economic theory. Moscow: Mir, 1999.

32 K. Valtukh, Information theory of value and the laws of a non-equilibrium economy. Moscow: Janus-K, 2001.

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