American Institute of Mathematical Sciences

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May  2008, 9(3&4, May): 431-461. doi: 10.3934/dcdsb.2008.9.431

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, Italy
2. 

Department of Mathematics, National Taiwan University, Taipei 106, Taiwan

Received  October 2006 Revised  July 2007 Published  February 2008

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.
Keywords: Singular perturbation, Melnikov function., homoclinic bifurcation, invariant manifolds.
Mathematics Subject Classification: Primary: 34E15, 34C23; Secondary: 37G2.
Citation: Flaviano Battelli, Ken Palmer. Heteroclinic connections in singularly perturbed systems. Discrete and Continuous Dynamical Systems - B, 2008, 9 (3&4, May) : 431-461. doi: 10.3934/dcdsb.2008.9.431
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