Heteroclinic connections in singularly perturbed systems

Flaviano Battelli; Ken Palmer

doi:10.3934/dcdsb.2008.9.431

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2008, Volume 9, Issue 3&4: 431-461. Doi: 10.3934/dcdsb.2008.9.431

This issue Previous Article Preface Next Article Nonautonomous finite-time dynamics

Heteroclinic connections in singularly perturbed systems

Flaviano Battelli^1, and
Ken Palmer^2,

1.
Dipartimento di Scienze Matematiche, Facoltà di Ingegneria, Università, Via Brecce Bianche, 1, 60100 Ancona
2.
Department of Mathematics, National Taiwan University, Taipei 106

Received: September 30, 2006

Revised: June 30, 2007

Published: April 2008

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Abstract

We consider a singularly perturbed system with two normally hyperbolic centre manifolds. We derive one bifurcation function, the zeros of which correspond to heteroclinic connections near such a connection for the unperturbed system, and a second bifurcation function the zeros of which correspond to the vectors in the intersection of the tangent spaces to the centre-unstable and centre-stable manifolds along the heteroclinic connections.

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Mathematics Subject Classification: Primary: 34E15, 34C23; Secondary: 37G20.

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