Homoclinic Orbits and Chaos in Nonlinear Dynamical Systems: Auxiliary Systems Method

被引：0

作者：

Grechko, D. A. ^{[1
,2
]}

Barabash, N., V ^{[1
,2
]}

Belykh, V. N. ^{[1
,2
]}

机构：

[1] Volga State Univ Water Transport, Nizhnii Novgorod 603950, Russia

[2] Lobachevsky State Univ Nizhny Novgorod, Nizhnii Novgorod 603022, Russia

来源：

LOBACHEVSKII JOURNAL OF MATHEMATICS | 2021年 / 42卷 / 14期

基金：

俄罗斯科学基金会;

关键词：

homoclinic orbit; Van der Pol-Duffing oscillator; Shilnikov chaos;

D O I：

10.1134/S199508022202007X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The auxiliary systems method in other words the method of two-dimensional comparison systems plays an essential role in the nonlocal bifurcational dynamical systems theory. In this paper we demonstrate this method in a particular case of 4-dimensional nonlinear dynamical system formed by a coupled Van der Pol-Duffing oscillator and a linear oscillator. For this system, using the auxiliary systems method, a rigorous proof of the existence of a homoclinic orbit of a saddle-focus is carried out for which the Shilnikov condition of chaos is satisfied. The paper is dedicated to the memory of Gennady A. Leonov, who made a significant contribution to the development of methods for the analytical study of dynamical systems.

引用

页码：3365 / 3371

页数：7

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