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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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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|Item Type:||Journal Article|
|Keywords:||Three-component reaction–diffusion system, Front solution, Geometric singular perturbation theory, Evans function, Center manifold reduction|
|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
|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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