Perturbation methods and the Melnikov functions for slowly varying oscillators

被引：6

作者：

Lakrad, F ^{[1
]}

Charafi, MM ^{[1
]}

机构：

[1] Polytech Inst, Casablanca, Morocco

来源：

CHAOS SOLITONS & FRACTALS | 2005年 / 25卷 / 03期

关键词：

D O I：

10.1016/j.chaos.2004.11.041

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A new approach to obtaining the Melnikov function for homoclinic orbits in slowly varying oscillators is proposed. The present method applies the Lindstedt-Poincare method to determine an approximation of homoclinic solutions. It is shown that the resultant Melnikov condition is the same as that obtained in the usual way involving distance functions in three dimensions by Wiggins and Holmes [Homoclinic orbits in slowly varying oscillators. SIAM J Math Anal 1987;18(3):612]. (c) 2005 Elsevier Ltd. All rights reserved.

引用

页码：675 / 680

页数：6

共 10 条

[1]

BEGLUND N, 1998, THESIS I PHYS THEORI

[2] Homoclinic connections in strongly self-excited nonlinear oscillators: The Melnikov function and the elliptic Lindstedt-Poincare method [J].