Homoclinic and heteroclinic solutions of cubic strongly nonlinear autonomous oscillators by hyperbolic Lindstedt-Poincaré method  

作　　者：SZE Kam Yim 

机构地区：[1]Department of Mechanical Engineering,The University of Hong Kong

出　　处：《Science China(Technological Sciences)》2010年第3期692-702,共11页中国科学（技术科学英文版）

基　　金：supported by the National Natural Science Foundation of China (Grant Nos.10672193, 10972240);Fu Lan Scholarship of Sun Yat-sen University,and the University of Hong Kong (CRGC grant)

摘　　要：The hyperbolic Lindstedt-Poincaré method is applied to determine the homoclinic and heteroclinic solutions of cubic strongly nonlinear oscillators of the form x + c1 x + c3 x 3= ε f (μ,x,x).In the method,the hyperbolic functions are employed instead of the periodic functions in the Lindstedt-Poincaré procedure.Critical value of parameter μ under which there exists homoclinic or heteroclinic orbit can be determined by the perturbation procedure.Typical applications are studied in detail.To illustrate the accuracy of the present method,its predictions are compared with those of Runge-Kutta method.The hyperbolic Lindstedt-Poincaré method is applied to determine the homoclinic and heteroclinic solutions of cubic strongly nonlinear oscillators of the form x + c1 x + c3 x 3= ε f (μ,x,x).In the method,the hyperbolic functions are employed instead of the periodic functions in the Lindstedt-Poincaré procedure.Critical value of parameter μ under which there exists homoclinic or heteroclinic orbit can be determined by the perturbation procedure.Typical applications are studied in detail.To illustrate the accuracy of the present method,its predictions are compared with those of Runge-Kutta method.

关 键 词：Lindstedt-Poincaré METHOD nonlinear AUTONOMOUS oscillator HOMOCLINIC ORBIT HETEROCLINIC ORBIT 

分 类 号：TN752[电子电信—电路与系统]