Predicting Homoclinic Bifurcations in Planar Autonomous Systems

被引：0
|
作者：
Mohamed Belhaq
Faouzi Lakrad
Abdelhak Fahsi
机构：
[1] Faculty of Sciences Ain Chock,Laboratory of Mechanics
[2] Group of Nonlinear Oscillations and Chaos,undefined
[3] Faculty of Sciences and Technique of Mohammedia,undefined
来源：
Nonlinear Dynamics | 1999年 / 18卷
关键词：
Periodic orbit; planar autonomous systems; homoclinic bifurcations; multiple scales technique; criteria;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
An analytical method to predict the homoclinic bifurcation in a planar autonomous self-excited weakly nonlinear oscillator is presented. The method is mainly based on the collision between the periodic orbit undergoing the homoclinic bifurcation and the saddle fixed point. To illustrate the analytical predictive criteria, two typical examples are investigated. The results obtained in this work are then compared to Melnikov's technique and to a previous criterion based on the vanishing of the frequency. Numerical simulations are also provided.
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页码：303 / 310
页数：7
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