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Digitale Medien

A Direct Approach to Homoclinic Orbits in the Fast Dynamics of Singularly Perturbed Systems (1999)

Beyn, Wolf-Jürgen ; Stiefenhofer, Matthias

Springer

Journal of dynamics and differential equations 11 (1999), S. 671-709

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Details

ISSN: 1572-9222

Schlagwort(e): Homoclinic orbits ; singular perturbations ; bifurcation ; FitzHugh–Nagumo system

Quelle: Springer Online Journal Archives 1860-2000

Thema: Mathematik

Notizen: Abstract Homoclinic orbits in the fast dynamics of singular perturbation problems are usually analyzed by a combination of Fenichel's invariant manifold theory with general transversality arguments (see Ref. 29 and the Exchange Lemma in Ref. 16). In this paper an alternative direct approach is developed which uses a two-time scaling and a contraction argument in exponentially weighted spaces. Homoclinic orbits with one last transition are treated and it is shown how ε-expansions can be extracted rigorously from this approach. The result is applied to a singularity perturbed Bogdanov point in the FitzHugh–Nagumo system.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1023/A:1022663512855

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