6533b834fe1ef96bd129ce9d

RESEARCH PRODUCT

Analysis of a slow–fast system near a cusp singularity

Henk W. BroerHildeberto Jardón-kojakhmetovRobert Roussarie

subject

Cusp (singularity)0209 industrial biotechnologyDifferential equationApplied Mathematics010102 general mathematicsMathematical analysis[MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS][ MATH.MATH-DS ] Mathematics [math]/Dynamical Systems [math.DS]02 engineering and technologyDynamical Systems (math.DS)01 natural sciencesPerturbation-theory020901 industrial engineering & automationSlow manifoldNormal form theoryFOS: MathematicsDifferential-equationsPerturbation theory (quantum mechanics)0101 mathematicsMathematics - Dynamical SystemsAnalysisCritical setMathematics

description

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.

yearjournalcountryeditionlanguage
2016-02-15
https://hal-univ-bourgogne.archives-ouvertes.fr/hal-01413158