余维4的Duffing-Van der Pol方程全局分岔分析

摘要

A Taylor series of Melnikov function was used to study bifurcation of nonlinear systems with high codimension here.The method was approved to be feasible by analyzing a generalized codimension-4 Duffing-Van der Pol equation.The results showed that there are phenomena of multiple limit cycles, single limit cycle and heteroclinic loop.Finally, numerical simulations verified the correctness of the theorectical analysis results.%采用级数展开形式的Melnikov函数解决高余维分岔问题.通过研究一类5次项和3次项共存,具有异宿轨的Duffing-Van der Pol方程的余维4全局分岔问题,得到了该系统的分岔方程及全局拓扑结构,说明了该方法的可行性.研究结果表明,该系统有单个极限环、单个异宿轨、异宿轨和极限环共存、两个极限环共存等情况.最后通过数值模拟验正了理论分析结果的正确性.