Numerical detection and continuation of homoclinic points and their bifurcations for maps and periodically forced systems

被引：14
|
作者：
Yagasaki, K [1 ]
机构：
[1] Gifu Univ, Dept Mech & Syst Engn, Gifu 5011193, Japan
来源：
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 1998年 / 8卷 / 07期
关键词：
D O I：
10.1142/S0218127498001285
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
This paper describes a driver HomMap to the standard local bifurcation software AUTO for numerical analysis of homoclinic and heteroclinic bifurcations in maps and periodically forced systems. The driver can detect loci of homoclinic points if the unstable or stable manifolds are of dimension one, and treat problems of two or more dimensions. The algorithms used and their implementations in AUTO with HomMap are explained. Three examples are given, namely the Henon map and the single and coupled Duffing oscillators, in order to demonstrate the usefulness and capabilities of the driver.
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页码：1617 / 1627
页数：11
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