Butterfly Catastrophe for Fronts in a Three-Component Reaction–Diffusion System

Martina Chirilus-Bruckner*, Arjen Doelman, Peter van Heijster, Jens D.M. Rademacher

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

10 Citations (Scopus)

Abstract

We study the dynamics of front solutions in a three-component reaction–diffusion system via a combination of geometric singular perturbation theory, Evans function analysis, and center manifold reduction. The reduced system exhibits a surprisingly complicated bifurcation structure including a butterfly catastrophe. Our results shed light on numerically observed accelerations and oscillations and pave the way for the analysis of front interactions in a parameter regime where the essential spectrum of a single front approaches the imaginary axis asymptotically.

Original languageEnglish
Pages (from-to)87-129
Number of pages43
JournalJournal of Nonlinear Science
Volume25
Issue number1
DOIs
Publication statusPublished - Feb 2014
Externally publishedYes

Keywords

  • Center manifold reduction
  • Evans function
  • Front solution
  • Geometric singular perturbation theory
  • Three-component reaction–diffusion system

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