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
收藏
页码：3365 / 3371
页数：7
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