Dynamical analysis of a cubic Lienard system with global parameters

作者：Chen Hebai^*; Chen Xingwu

来源：Nonlinearity, 2015, 28(10): 3535-3562.

DOI：10.1088/0951-7715/28/10/3535

• bifurcation diagram
• global phase portrait
• homoclinic loop
• limit cycle

In this paper we investigate the dynamical behaviour of a cubic Lienard system with global parameters. After analysing the qualitative properties of all the equilibria and judging the existences of limit cycles and homoclinic loops for the whole parameter plane, we give the bifurcation diagram and phase portraits. Phase portraits are global if there exist limit cycles and local otherwise. We prove that parameters lie in a connected region, not just on a curve, usually in the parameter plane when the system has one homoclinic loop. Moreover, for global parameters we give a positive answer to conjecture 3.2 of (1998 Nonlinearity 11 1505-19) in the case of exactly two equilibria about the existence of some function whose graph is exactly the surface of double limit cycles.

• 出版日期2015-10
• 单位四川大学; 西南交通大学