Butterfly catastrophe for fronts in a three-component reaction–diffusion system

Chirilus-Bruckner, Martina, Doelman, Arjen, van Heijster, Peter, & Rademacher, Jens D.M. (2015) Butterfly catastrophe for fronts in a three-component reaction–diffusion system. Journal of Nonlinear Science, 25(1), pp. 87-129.

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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.

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ID Code: 79686
Item Type: Journal Article
Refereed: Yes
Keywords: Three-component reaction–diffusion system, Front solution, Geometric singular perturbation theory, Evans function, Center manifold reduction
DOI: 10.1007/s00332-014-9222-9
ISSN: 0938-8974
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > PURE MATHEMATICS (010100) > Ordinary Differential Equations Difference Equations and Dynamical Systems (010109)
Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > PURE MATHEMATICS (010100) > Partial Differential Equations (010110)
Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > APPLIED MATHEMATICS (010200)
Divisions: Current > QUT Faculties and Divisions > Science & Engineering Faculty
Past > Schools > Mathematical Sciences
Funding:
  • DEUTSCHE FORSCHUNGSG/CH 957/1-1
Copyright Owner: Copyright 2014 Springer Science+Business Media New York
Copyright Statement: The final publication is available at Springer via http://dx.doi.org/10.1007/s00332-014-9222-9
Deposited On: 05 Jan 2015 23:24
Last Modified: 05 Feb 2015 17:27

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