ANDRONOV–HOPF BIFURCATION OF HIGHER CODIMENSIONS IN A LIÉNARD SYSTEM-Reference-Cited by-同舟云学术

ANDRONOV–HOPF BIFURCATION OF HIGHER CODIMENSIONS IN A LIÉNARD SYSTEM

Published:2012-11 Issue:11 Volume:22 Page:1250271
ISSN:0218-1274
Container-title:International Journal of Bifurcation and Chaos
language:en
Short-container-title:Int. J. Bifurcation Chaos

Author:

GRIN ALEXANDER¹,SCHNEIDER KLAUS R.²

Affiliation:

1. Grodno State University, Ozheshko Street 22, 230023 Grodno, Belarus

2. Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, D-10117 Berlin, Germany

Abstract

We study a polynomial Liénard system depending on three parameters a, b, c and exhibiting the following properties: (i) The origin is the unique equilibrium for all parameters. (ii) If a crosses zero, then the origin changes its stability, and Andronov–Hopf bifurcation arises. We consider a as control parameter and investigate the dependence of Andronov–Hopf bifurcation on the "unfolding" parameters b and c. We establish and describe analytically the existence of surfaces and curves located near the origin in the parameter space connected with the existence of small-amplitude limit cycles of multiplicity two and three (existence of degenerate Andronov–Hopf bifurcation).

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modeling and Simulation,Engineering (miscellaneous)

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218127412502719

Reference15 articles.

1. The number of small-amplitude limit cycles of Liénard equations

2. Comparaison de la Méthode des Constantes de Lyapunov et de la Bifurcation de Hopf*

3. On the construction of bifurcation curves related to limit cycles of multiplicity three for planar vector fields

Cited by 1 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. On the construction of bifurcation curves related to limit cycles of multiplicity three for planar vector fields;Journal of Computational and Applied Mathematics;2013-01