Analysis of a slow–fast system near a cusp singularity

Abstract : 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. (C) 2015 Elsevier Inc. All rights reserved.
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Journal of Differential Equations, Elsevier, 2016, 260 (4), pp.3785 - 3843. 〈http://www.sciencedirect.com/science/article/pii/S0022039615005884〉. 〈10.1016/j.jde.2015.10.045〉
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https://hal-univ-bourgogne.archives-ouvertes.fr/hal-01413158
Contributeur : Imb - Université de Bourgogne <>
Soumis le : vendredi 9 décembre 2016 - 14:22:46
Dernière modification le : lundi 9 octobre 2017 - 13:18:03

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H. Jardón-Kojakhmetov, Henk W. Broer, R. Roussarie. Analysis of a slow–fast system near a cusp singularity. Journal of Differential Equations, Elsevier, 2016, 260 (4), pp.3785 - 3843. 〈http://www.sciencedirect.com/science/article/pii/S0022039615005884〉. 〈10.1016/j.jde.2015.10.045〉. 〈hal-01413158〉

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