余维4的Duffing-Van der Pol方程全局分岔分析  

Global bifurcations for a generalized codimension-4 Duffing-Van der Pol equation

作　　者：刘延彬[1] 陈予恕[1] 

机构地区：[1]哈尔滨工业大学航天学院,哈尔滨150001

出　　处：《振动与冲击》2011年第1期69-72,110,共5页Journal of Vibration and Shock

基　　金：国家自然科学基金重点资助项目(10632040)

摘　　要：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。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.

关 键 词：全局分岔 余维 MELNIKOV函数 异宿轨 

分 类 号：O322[理学—一般力学与力学基础] O415.6[理学—力学]