The construction of homoclinic and heteroclinic orbitals in asymmetric strongly nonlinear systems based on the Pad'e approximant  

作　　者：冯晶晶 张琪昌 王炜 

机构地区：[1]Department of Mechanics,School of Mechanical Engineering,Tianjin University [2]Tianjin Key Labortory of Nonlinear Dynamics and Chaos Control,Tianjin University [3]State Key Laboratory of Engines,Tianjin University

出　　处：《Chinese Physics B》2011年第9期19-29,共11页中国物理B（英文版）

基　　金：Project supported by the National Natural Science Foundation of China (Grant Nos.11072168 and 10872141)

摘　　要：In this paper, the extended Pade approximant is used to construct the homoclinic and the heteroclinic trajectories in nonlinear dynamical systems that are asymmetric at origin. Meanwhile, the conservative system, the autonomous system, and the nonautonomous system equations with quadratic and cubic nonlinearities are considered. The disturbance parameter ~ is not limited to being small. The ranges of the values of the linear and the nonlinear term parameters, which are variables, can be determined when the boundary values are satisfied. New conditions for the potentiality and the convergence are posed to make it possible to solve the boundary-value problems formulated for the orbitals and to evaluate the initial amplitude values.In this paper, the extended Pade approximant is used to construct the homoclinic and the heteroclinic trajectories in nonlinear dynamical systems that are asymmetric at origin. Meanwhile, the conservative system, the autonomous system, and the nonautonomous system equations with quadratic and cubic nonlinearities are considered. The disturbance parameter ~ is not limited to being small. The ranges of the values of the linear and the nonlinear term parameters, which are variables, can be determined when the boundary values are satisfied. New conditions for the potentiality and the convergence are posed to make it possible to solve the boundary-value problems formulated for the orbitals and to evaluate the initial amplitude values.

关 键 词：BIFURCATION Pade approximant strongly nonlinearity homoclinic and heteroclinic orbitals 

分 类 号：N93[自然科学总论]