无小参数系统的混沌与亚谐共振

Chaos and Sub-Harmonic Resonance of Nonlinear System Without Small Parameters

Melnikov方法是判别混沌和亚谐共振的一种重要方法.传统的Melnikov方法依赖于小参数,在大多数实际物理系统中,小参数是不存在的.因此,传统的Melnikov方法不能应用于强非线性系统.为了摆脱小参数对Melnikov方法的限制,采用同伦分析将Melnikov方法拓展到强非线性系统,且采用该方法研究了一个强非线性系统的亚谐共振与混沌,解析结果和数值结果相互吻合,说明了该方法的有效性.

Melnikov method was especially important to detect the presence of transverse homoclinic orbits and occurrence of homoclinic bifurcations. Unfortunately traditional Melnikov methods strongly depend on small parameter,which could not exist in most of the practice physical systems. Those methods were limited in dealing with the system with strongly nonlinear. A procedure to study the chaos and sub-harmonic resonance of strongly nonlinear practice systems by employing homotopy method which was used to extend Melnikov functions to strongly nonlinear systems was presented. Applied to a given example,the procedure shows the efficiencies in the comparison of the theoretical results and numerical simulation.