Stability and bifurcation analysis in the delay-coupled van der Pol oscillators

被引：25

作者：

Zhang, Jianming ^{[1
,2
]}

Gu, Xinsheng ^{[1
]}

机构：

[1] E China Univ Sci & Technol, Res Inst Automat, Shanghai 200237, Peoples R China

[2] Zhejiang Sic Tech Univ, Dept Math, Hangzhou 310018, Zhejiang, Peoples R China

来源：

APPLIED MATHEMATICAL MODELLING | 2010年 / 34卷 / 09期

关键词：

Coupled van der Pol equations; Stability switches; Hopf bifurcation; Normal form; LIMIT-CYCLE OSCILLATORS; HOPF BIFURCATIONS; FEEDBACK; EQUATIONS; DYNAMICS;

D O I：

10.1016/j.apm.2009.10.037

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

In this paper, the dynamics of a system of two van der Pol equations with a finite delay are investigated. We show that there exist the stability switches and a sequence of Hopf bifurcations occur at the zero equilibrium when the delay varies. Using the theory of normal form and the center manifold theorem, the explicit expression for determining the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions are derived. (C) 2009 Elsevier Inc. All rights reserved.

引用

页码：2291 / 2299

页数：9

共 15 条

[1] Distributed delays facilitate amplitude death of coupled oscillators [J].

Atay, FM .

PHYSICAL REVIEW LETTERS, 2003, 91 (09)

[2] Van der Pol's oscillator under delayed feedback [J].

Atay, FM .

JOURNAL OF SOUND AND VIBRATION, 1998, 218 (02) :333-339

[3]

Hale J.K., 1977, THEORY FUNCTIONAL DI

[4]

Hassard B.D., 1981, Theory and Applications of Hopf Bifurcation

[5] Existence of limit cycles for coupled van der Pol equations [J].

Hirano, N ;

Rybicki, S .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2003, 195 (01) :194-209

[6] Bifurcation analysis in van der Pol's oscillator with delayed feedback [J].

Jiang, Weihua ;

Wei, Junjie .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2008, 213 (02) :604-615

[7] Dynamics of two delay coupled van der Pol oscillators [J].

Li, Xinye ;

Ji, J. C. ;

Hansen, Colin H. .

MECHANICS RESEARCH COMMUNICATIONS, 2006, 33 (05) :614-627

[8] Time delay effects on coupled limit cycle oscillators at Hopf bifurcation [J].

Reddy, DVR ;

Sen, A ;

Johnston, GL .

PHYSICA D, 1999, 129 (1-2) :15-34

[9] Time delay induced death in coupled limit cycle oscillators [J].

Reddy, DVR ;

Sen, A ;

Johnston, GL .

PHYSICAL REVIEW LETTERS, 1998, 80 (23) :5109-5112

[10] Dynamics of three coupled van der Pol oscillators with application to circadian rhythms [J].

Rompala, Kevin ;

Rand, Richard ;

Howland, Howard .

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2007, 12 (05) :794-803

← 1 2 →