一类拟 Hamilton 碰振系统的全局分岔及多解共存现象分析

Analysis of the Global Bifurcations and Coexistence of Multiple Solutions for a General Quasi-Hamiltonian Vibro-impact System

研究了一类拟Hamilton碰振系统的全局动力学特性,参照同宿轨道的Melnikov函数形式,构造了周期轨道次谐Melnikov函数.并用一类拟Hamilton碰振系统详细介绍了其计算方法和运用,数值结果验证了构造的次谐Melnikov函数的有效性.另外用改进的胞映射方法对这类系统的全局分岔和多解共存现象进行了分析,发现随着外激励力的变动吸引子数量发生变化,各个吸引域形态复杂且相互缠绕.

This paper studied the global dynamic properties of a quasi-Hamiltonian vibro-impact sys-tem.By referring to Melnikov function for homoclinic orbit in the quasi-Hamiltonian system,the subhar-monic Melnikov function for periodic orbit was constructed.A quasi-Hamiltonian vibro-impact system was given to illustrate the application of the procedures,and the validity of the function was verified with nu-merical results.At the same time,the global bifurcations and coexistence of multiple solutions for this vi-bro-impact system were analyzed in the improved cell mapping method.The number of coexistent attractor changes with the change of external excitation force,and domains of attraction with complicated fractal boundaries are intertwined.