Generalized hyperbolic perturbation method for homoclinic solutions of strongly nonlinear autonomous systems

被引：15

作者：

Chen, Yang-yang ^{[2
]}

Yan, Le-wei ^{[3
]}

Sze, Kam-yim ^{[4
]}

Chen, Shu-hui ^{[1
]}

机构：

[1] Sun Yat Sen Univ, Dept Appl Mech & Engn, Guangzhou 510275, Guangdong, Peoples R China

[2] Guangzhou Univ, Key Lab Vibrat Control & Struct Safety, Minist Educ China, Guangzhou 510405, Guangdong, Peoples R China

[3] Guangzhou Univ, Dept Engn Mech, Guangzhou 510405, Guangdong, Peoples R China

[4] Univ Hong Kong, Dept Mech Engn, Pokfulam, Hong Kong, Peoples R China

来源：

APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION | 2012年 / 33卷 / 09期

基金：

中国国家自然科学基金;

关键词：

generalized hyperbolic perturbation method; nonlinear autonomous system; homoclinic solution; LIMIT-CYCLES; BIFURCATIONS; OSCILLATORS; CONSTRUCTION; ORBITS;

D O I：

10.1007/s10483-012-1611-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A generalized hyperbolic perturbation method is presented for homoclinic solutions of strongly nonlinear autonomous oscillators, in which the perturbation procedure is improved for those systems whose exact homoclinic generating solutions cannot be explicitly derived. The generalized hyperbolic functions are employed as the basis functions in the present procedure to extend the validity of the hyperbolic perturbation method. Several strongly nonlinear oscillators with quadratic, cubic, and quartic nonlinearity are studied in detail to illustrate the efficiency and accuracy of the present method.

引用

页码：1137 / 1152

页数：16

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