ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)


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Kruglov V. P., Kuptsov P. V. Theoretical models of physical systems with rough chaos. Izvestiya VUZ. Applied Nonlinear Dynamics, 2021, vol. 29, iss. 1, pp. 35-77. DOI: 10.18500/0869-6632-2021-29-1-35-77

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
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Language: 
Russian
Article type: 
Review
UDC: 
530.182

Theoretical models of physical systems with rough chaos

Autors: 
Kruglov Vjacheslav Pavlovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Kuptsov Pavel Vladimirovich, Yuri Gagarin State Technical University of Saratov
Abstract: 

The purpose of this review is to present in a unified manner the latest results on mathematical modeling of rough hyperbolic chaos in systems of various physical nature. Main research Methods are the numerical solution of systems of differential equations and partial differential equations, numerical extraction of the phase of oscillatory processes or spatial patterns, calculating of Lyapunov exponents, and studying the mutual arrangement of the stable and unstable manifolds of chaotic trajectories, the calculation of Gaussian curvature of surfaces. These procedures allow to reveal the typical attributes of rough hyperbolic chaos. Results reproduce the studies of already known phenomena, however, their qualitative explanation and quantitative confirmation are given in in a more detailed form, in accordance with the development of ideas about them. Conclusion. Methodologically the proposed review article may be interesting for undergraduate and graduate students in terms of studying the principles of construction and analysis of systems with chaotic behavior.

Acknowledgments: 
Работа В.П. Круглова (Раздел 2, Модели пространственно распределенных систем с аттрактором типа Смейла–Вильямса) поддержана грантом РНФ № 19-11-00280. Работа П.В. Купцова выполнена в рамках государственного задания Института радиотехники и электроники им. В.А. Котельникова РАН.
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Received: 
16.11.2020
Accepted: 
15.12.2020
Published: 
01.02.2021