一类非对称Lienard系统的分支及稳定性

Bifurcations and stability for a class of non-symmetric Lienard equations

研究了一类非中心对称的Lienard多项式系统的稳定性和分支问题。利用一阶Melnikov函数和Picard-Fuchs方程法,得到了Hopf分支、同宿分支以及二重闭轨分支的存在条件和分支曲线计算公式,在此基础上,结合数值方法给出了各种分支的分支图和相轨线结构。

The dynamics of a class of Lienard equations with non-symmetric terms are investigated.Using Melnikov function and Picard-Fuchs equation,conditions for the existence and the formula for calculating bifurcation values of Hopf,homoclinic orbit and double limit cycle bifurcations are derived.Moreover,the complete bifurcation diagrams and phase portraits are obtained.The results show that the double limit cycle bifurcations occur at the curve between two critical points if the system contains the non-symmetric terms.