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

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...

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Published inChinese physics B Vol. 20; no. 9; pp. 19 - 29
Main Author 冯晶晶 张琪昌 王炜
Format Journal Article
LanguageEnglish
Published IOP Publishing 01.09.2011
Subjects
Approximants
Asymmetry
Boundary value problems
Construction
Dynamical systems
Mathematical analysis
Nonlinear dynamics
Nonlinearity
Padé逼近
不对称
异宿轨道
强非线性系统
边界值问题
非线性动力系统
非线性方程
非自治系统
Online AccessGet full text
ISSN1674-1056
2058-3834
DOI10.1088/1674-1056/20/9/090202

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Summary: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.
Bibliography: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.
Feng Jing-Jing Zhang Qi-Chang and Wang Wei a） Department of Mechanics, School of Mechanical Engineering, Tianjin University, Tianjin 300072, China b） Tianjin Key Labortory of Nonlinear Dynamics and Chaos Control, Tianjin University, Tianjin 300072, China c） State Key Laboratory of Engines, Tianjin University, Tianfin 300072, China
11-5639/O4
bifurcation, Pade approximant, strongly nonlinearity, homoclinic and heteroclinic orbitals
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ISSN:1674-1056
2058-3834
DOI:10.1088/1674-1056/20/9/090202