Global bifurcation studies of a cubic Liénard system

Release time:2020-12-01

DOI number:10.1016/j.jmaa.2020.124810

Journal:Journal of Mathematical Analysis and Applications

Abstract:In recent decades much attention has been paid to polynomial Liénard systems. Cubic ones are such systems with a cubic restoring and quadratic damping; for example, the famous FitzHugh-Nagumo system can be transformed into a cubic Liénard system. For the three-parameter family of cubic Liénard systems, the case with a positive restoring leading coefficient was solved. In this paper we will investigate the case when the leading coefficient of the restoring is negative, we will show that saddle-node bifurcations, pitchfork bifurcations, Hopf bifurcations, homoclinic bifurcations, and heteroclinic bifurcations will occur through a global analysis and present a global bifurcation diagram with global phase portraits depicted in Poincaré disks. Finally, some main results are demonstrated by numerical simulations.

Co-author:Zhu Huaiping*

First Author:Chen Hebai

Indexed by:Journal paper

Discipline:数学

Document Type:J

Translation or Not:no

Date of Publication:2020-11-30

Included Journals:SCI