Application of Chaos Theory, Thermodynamics and AI in the Analysis of the Behavior of Complex Systems

This chapter is devoted to the theoretical and practical aspects of the application of chaos theory. The objects of research are multidimensional nonlinear information systems. Methods for studying the behavior of multidimensional nonlinear information systems operating within the framework of the Open System are presented. It should be noted that the physics of open systems develops a unified approach to the description of a wide variety of non-linear phenomena. Using the achievements of such scientific fields as chaos theory, thermodynamics, visual thinking and artificial intelligence, it is possible to discover hidden patterns and additional knowledge when studying such complex systems. In studies of the dynamics of complex systems, various characteristic indicators are used. To study the development processes of a dynamic system in time, Poincare return times, Lyapunov exponents, Tsallis entropy, fractal dimensions of the system, stability parameters, etc. are used. In the final part of the chapter, all these informative characteristic indicators of the system under study are proposed to be used for the input layer of the Recurrent Neural Network of the Deep Learning Artificial Intelligence algorithm. The issues of visualization of measurement results and information processing using the "Visual Thinking" technology are considered. In the examples given, due attention is paid to the issues of modern visualization, which is the basis for the implementation of the "Visual Thinking" technology in research activities. The analysis of visual information characterizing the dynamics of the parameters of the system under study will increase the speed of assessing its behavior, as well as the validity of the decisions made on its control.