Generalized scenarios of transition to chaos in ideal dynamic systems

Authors

DOI:

https://doi.org/10.20535/SRIT.2308-8893.2024.3.04

Keywords:

ideal dynamic system, regular and chaotic attractors, generalized intermittency scenario

Abstract

The implementation of a new scenario of transition to chaos in the classical Lorenz system has been discovered. Signs of the presence of an implementation of the generalized intermittency scenario for dynamic systems are described. Phase-parametric characteristics, Lyapunov characteristic exponents, distributions of invariant measures, and Poincaré sections are constructed and analyzed in detail, which confirm the implementation of the generalized intermittency scenario in an ideal Lorenz system.

Author Biographies

Oleksii Horchakov, Institute of Mathematics of NASU, Kyiv

Ph.D. student at the Department of Mathematical Problems of Mechanics and Control Theory of the Institute of Mathematics of NASU, Kyiv, Ukraine.

Aleksandr Shvets, National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", Kyiv

Doctor of Physical and Mathematical Sciences, a professor at the Department of Mathematical Physics and Differential Equations of the Faculty of Physics and Mathematics of the National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", Kyiv, Ukraine.

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Published

2024-09-28

Issue

No. 3 (2024)

Section

Methods of optimization, optimum control and theory of games

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