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Zoekopdracht: faculteit: "FNWI" en publicatiejaar: "2008"

AuteursP. van Heijster, A. Doelman, T.J. Kaper
TitelPulse dynamics in a three-component system: Stability and bifurcations
TijdschriftPhysica D
Jaargang237
Jaar2008
Nummer24
Pagina's3335-3368
ISSN01672789
FaculteitFaculteit der Natuurwetenschappen, Wiskunde en Informatica
Instituut/afd.FNWI: Korteweg-de Vries Institute for Mathematics (KdVI)
SamenvattingIn this article, we analyze the stability and the associated bifurcations of several types of pulse solutions in a singularly perturbed three-component reaction–diffusion equation that has its origin as a model for gas discharge dynamics. Due to the richness and complexity of the dynamics generated by this model, it has in recent years become a paradigm model for the study of pulse interactions. A mathematical analysis of pulse interactions is based on detailed information on the existence and stability of isolated pulse solutions. The existence of these isolated pulse solutions is established in previous work. Here, the pulse solutions are studied by an Evans function associated to the linearized stability problem. Evans functions for stability problems in singularly perturbed reaction–diffusion models can be decomposed into a fast and a slow component, and their zeroes can be determined explicitly by the NLEP method. In the context of the present model, we have extended the NLEP method so that it can be applied to multi-pulse and multi-front solutions of singularly perturbed reaction–diffusion equations with more than one slow component. The brunt of this article is devoted to the analysis of the stability characteristics and the bifurcations of the pulse solutions. Our methods enable us to obtain explicit, analytical information on the various types of bifurcations, such as saddle-node bifurcations, Hopf bifurcations in which breathing pulse solutions are created, and bifurcations into travelling pulse solutions, which can be both subcritical and supercritical.
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