Science and Education in Karakalpakstan issn 2181-9203 Science Magazine chief editor

Science and Education in Karakalpakstan. 2023 №2/1 ISSN 2181-9203 
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Studies in Researching the Nature of Complexity and the Association for Complex Thinking, 
founded by the French philosopher and sociologist E.Moren, explores complexity in a variety of 
ways. The Institute for Mathematical Research of Complex Systems, founded in 1995 in the 
Russian Federation, deals with the problems of mathematical modeling of nonlinear dynamic 
systems in nature and society. Many aspects of complex systems are studied at the Philosophical-
Methodological and Interdisciplinary Approach Center of the Institute of Philosophy of the National 
Academy of Sciences of Belarus. 
Complexity research is a multifaceted problem. In this regard, there are different concepts 
for analyzing the phenomenon of complexity. That is, several research programs of complexity 
research have been developed in modern philosophy. For example, G. Hacken, I. Prigogine, E. 
Moren, U. Maturana and F. Varella, E.N. Among these are a number of concepts in Knyazeva et al. 
Various aspects of the phenomenon of complexity are studied in these concepts. 
A number of scientific results have been obtained as a result of researches conducted in the 
world related to the problem of complexity, modeling of complex systems, theory of nonlinear 
dynamics and systematic thinking: complex system problems (Center for the study of Complex 
systems); the principles of complex thinking were formed (Association Internationale poul la 
Pensee Complexe, France); complex systems, theory of nonlinear dynamics, natural and scientific 
foundations of synergetics have been developed (German Society of Complex Systems and 
Nonlinear Dynamics Universitat Stuttgart); research is being conducted on complex and systematic 
thinking problems (Munich Technological University); Philosophical-methodological and 
epistemological aspects of complex systems are studied (National University of Uzbekistan, 
Karakalpak Scientific Research Institute of Natural Sciences of UzRSA). 
Synergetics method, adaptation theory, transition from abstract to concrete, from concrete to 
abstract, principles of objectivity and systematicity were used as a methodological strategy in 
researching the dynamics of complex socio-economic systems. 
Two main trends can be distinguished in the dynamics of socio-economic systems. The first 
tendency is the preservation of the system, the second is the tendency to change the system. The 
adaptation mechanism works for the first trend of this dynamic, while the bifurcation mechanism 
works for the second one. Therefore, the adaptive model and the bifurcation model are typical for 
the dynamics of socio-economic systems. 
What is the significance of the bifurcation model in the dynamics of socio-economic 
systems? Theories of bifurcations and catastrophes are one of the effective methods for modeling 
nonlinear complex socio-economic systems. The reason is that socio-economic systems do not 
always have balance, order, linearity, and stability. In the dynamics of this system, chaotic, 
destructive situations are also legal [5]. Catastrophe is a jump-like change caused by an unexpected 
response of the system to a change in external influence. In the modeling of such processes, the 
theory of bifurcation and collapse in mathematics was developed by R. Thom and V. I. Arnold. 
These theories describe the origin of discontinuity, that is, discrete structure, from discontinuity in 
the system. The term bifurcation (branching, duality) is used to explain the qualitative restructuring 
of various systems due to changes in system parameters. As a simple example of a bifurcation state, 
we can imagine a body jumping into another state under the influence of an unexpected external 
weight. At the bifurcation point, a choice between two possible solutions appears. This critical 
value is called the bifurcation point. After the bifurcation, there will probably be multiple structures 
within which the system will begin to develop again. It is difficult to predict which of these 
structures will manifest. Because there are random effects and fluctuations of the external 
environment during departure from the threshold state, which determines the choice of this 
structure. This bifurcation mechanism plays a special role in the development of our world. 

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