Canards and horseshoes in the forced van der Pol equation

被引：0

作者：

Weckesser, W ^{[1
]}

机构：

[1] Colgate Univ, Dept Math, Hamilton, NY 13346 USA

来源：

EQUADIFF 2003: INTERNATIONAL CONFERENCE ON DIFFERENTIAL EQUATIONS | 2005年

关键词：

D O I：

10.1142/9789812702067_0155

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Cartwright and Littlewood discovered "chaotic" solutions in the periodically forced van der Pol equation in the 1940's. Subsequent work by Levinson, Levi, and others has made this singularly perturbed system one of the archetypical dissipative systems with chaotic dynamics. Despite the extensive history of this system, many questions concerning its bifurcations and chaotic dynamics remain. We use a combination of analysis of the singular limit and numerical simulation to describe a horseshoe map that arises in the three-dimensional phase space. The canards that form at a "folded saddle" play a crucial role in this analysis.

引用

页码：931 / 936

页数：6