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Article Dans Une Revue Journal of Differential Equations Année : 2016

Analysis of a slow–fast system near a cusp singularity

Résumé

This paper studies a slow–fast system whose principal characteristic is that the slow manifold is given by the critical set of the cusp catastrophe. Our analysis consists of two main parts: first, we recall a formal normal form suitable for systems as the one studied here; afterwards, taking advantage of this normal form, we investigate the transition near the cusp singularity by means of the blow up technique. Our contribution relies heavily in the usage of normal form theory, allowing us to refine previous results.

Dates et versions

hal-01413158 , version 1 (09-12-2016)

Identifiants

Citer

H. Jardón-Kojakhmetov, Henk W. Broer, Robert Roussarie. Analysis of a slow–fast system near a cusp singularity. Journal of Differential Equations, 2016, 260 (4), pp.3785-3843. ⟨10.1016/j.jde.2015.10.045⟩. ⟨hal-01413158⟩
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