Work

Weakly coupled two-slow–two-fast systems, folded singularities and mixed mode oscillations

Year: 2014

Type: article

Abstract: We study mixed mode oscillations (MMOs) in systems of two weakly coupled slow/fast oscillators. We focus on the existence and properties of a folded singularity, called folded saddle node of type II (FSN II), that allows the emergence of MMOs in the presence of a suitable global return mechanism. As FSN II corresponds to a transcritical bifurcation for a desingularized reduced system, we prove that, under certain non-degeneracy conditions, such a transcritical bifurcation exists. We then apply this result to the case of two coupled systems of FitzHugh–Nagumo type. This leads to a non-trivial condition on the coupling that enables the existence of MMOs.

Source: Nonlinearity

DOI: 10.1088/0951-7715/27/7/1555

Authors: M Krupa, B Ambrosio, M A Aziz-Alaoui

Institutions: Institut national de recherche en sciences et technologies du numérique, Centre National de la Recherche Scientifique, Normandie Université, Laboratoire de Mathématiques Appliquées du Havre

Language: English

Topic: Advanced Differential Equations and Dynamical Systems

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funder: Région Normandie

OpenAlex ID: W1575250855

FWCI: 3.236

Cites: 19

Cited by: 31

Related to: 10