On computing  heteroclinic trajectories of non-autonomous maps

Thorsten Hüls; Yongkui Zou

doi:10.3934/dcdsb.2012.17.79

Article Contents

2012, Volume 17, Issue 1: 79-99. Doi: 10.3934/dcdsb.2012.17.79

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On computing heteroclinic trajectories of non-autonomous maps

Thorsten Hüls^1, and
Yongkui Zou^2,

1.
Department of Mathematics, Bielefeld University, POB 100131, 33501 Bielefeld
2.
Department of Mathematics, Jilin University, Changchun 130012

Received: January 2011

Revised: June 2011

Published: January 2012

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Abstract

We propose an adequate notion of a heteroclinic trajectory in non-autonomous systems that generalizes the notion of a heteroclinic orbit of an autonomous system. A heteroclinic trajectory connects two families of semi-bounded trajectories that are bounded in backward and forward time. We apply boundary value techniques for computing one representative of each family. These approximations allow the construction of projection boundary conditions that enable the calculation of a heteroclinic trajectory with high accuracy. The resulting algorithm is applied to non-autonomous toy models as well as to an example from mathematical biology.

Keywords:

Non-autonomous discrete time dynamical systems,
heteroclinic connection,
numerical approximation,
boundary value problems,
error analysis.

Mathematics Subject Classification: Primary: 70K44, 37B55; Secondary: 34C37.

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