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RESEARCH PAPERS

Chaos and Three-Dimensional Horseshoes in Slowly Varying Oscillators

[+] Author and Article Information
Stephen Wiggins

Applied Mechanics 104-44, California Institute of Technology, Pasadena, CA 91125

Steven W. Shaw

Dept. of Mechanical Engineering, Michigan State University, East Lansing, MI 48824

J. Appl. Mech 55(4), 959-968 (Dec 01, 1988) (10 pages) doi:10.1115/1.3173748 History: Received October 29, 1986; Revised February 10, 1988; Online July 21, 2009

Abstract

We present general results pertaining to chaotic motions in a class of systems termed slowly varying oscillators which consist of weakly perturbed single-degree-of-freedom systems in which parameters vary slowly in time according to an additional equation of motion. Our results include an analytical method for detecting transversal intersections of stable and unstable manifolds (typically a necessary condition for chaotic motions to exist) and a detailed description of the chaotic dynamics that occur when this situation exists.

Copyright © 1988 by ASME
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