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
相关论文
共 14 条
[1]   Chaotic driven maps: Non-stationary hyperbolic attractor and hyperchaos [J].
Barabash, Nikita, V ;
Belykh, Vladimir N. .
EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS, 2020, 229 (6-7) :1071-1081
[2]  
Belykh V., 2018, DINAMICHESKIE SISTEM, V8, P373
[3]   Chaotic dynamics of two Van der Pol-Duffing oscillators with Huygens coupling [J].
Belykh, V. N. ;
Pankratova, E. V. .
REGULAR & CHAOTIC DYNAMICS, 2010, 15 (2-3) :274-284
[4]  
Belykh V.N., 1997, P STEKLOV I, V216, P20
[5]  
Belykh V.N., 2000, T AMS 2, V200, P51
[6]  
Belykh V. N., 1984, Differ. Uravn, V20, P1666
[7]   Shilnikov Chaos in Oscillators with Huygens Coupling [J].
Belykh, Vladimir N. ;
Pankratova, Evgeniya V. .
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2014, 24 (08)
[8]  
Belyustina L., 1973, Differentsial'nye Uravneniya, V9, P595
[9]  
Chua L.O., 2001, Methods of Qualitative Theory in Nonlinear Dynamics
[10]  
Reitmann V., 2018, NONLOCAL METHODS PEN
12