The numerical detection of connecting orbits

Pages: 125 - 135, Volume 1, Issue 1, February 2001

doi:10.3934/dcdsb.2001.1.125       Abstract        Full Text (615.8K)       Related Articles

Michael Dellnitz - Department of Mathematics and Computer Science, University of Paderborn, D-33095 Paderborn, Germany (email)
O. Junge - Department of Mathematics and Computer Science, University of Paderborn, D-33095 Paderborn, Germany (email)
B Thiere - Department of Mathematics and Computer Science, University of Paderborn, D-33095 Paderborn, Germany (email)

Abstract: We present a new technique for the numerical detection and localization of connecting orbits between hyperbolic invariant sets in parameter dependent dynamical systems. This method is based on set-oriented multilevel methods for the computation of invariant manifolds and it can be applied to systems of moderate dimension. The main idea of the algorithm is to detect intersections of coverings of the stable and unstable manifolds of the invariant sets on different levels of the approximation. We demonstrate the applicability of the new method by three examples.

Keywords:  Heteroclinic orbit, detection of connecting orbits.
Mathematics Subject Classification:  37M20, 65P30, 37G20.

Published: January 2001.