无小参数系统的混沌与亚谐共振

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．     

Analysis method of chaos and sub-harmonic resonance of nonlinear system without small parameters

The Melnikov method is important for detecting the presence of transverse homoclinic orbits and the occurrence of homoclinic bifurcations.Unfortunately,the traditional Melnikov methods strongly depend on small parameters,which do not exist in most practical systems.Those methods are limited in dealing with the systems with strong nonlinearities.This paper presents a procedure to study the chaos and sub-harmonic resonance of strongly nonlinear practical systems by employing a homotopy method that is used ...