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Basin of Attraction of Solutions with Pattern Formation in Slow–Fast Reaction–Diffusion Systems

Basin of Attraction of Solutions with Pattern Formation in Slow–Fast Reaction–Diffusion Systems This article is devoted to the characterization of the basin of attraction of pattern solutions for some slow–fast reaction–diffusion systems with a symmetric property and an underlying oscillatory reaction part. We characterize some subsets of initial conditions that prevent the dynamical system to evolve asymptotically toward solutions which are homogeneous in space. We also perform numerical simulations that illustrate theoretical results and give rise to symmetric and non-symmetric pattern solutions. We obtain these last solutions by choosing particular random initial conditions. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Biotheoretica Springer Journals

Basin of Attraction of Solutions with Pattern Formation in Slow–Fast Reaction–Diffusion Systems

Acta Biotheoretica , Volume 64 (4) – Oct 21, 2016

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References (35)

Publisher
Springer Journals
Copyright
Copyright © 2016 by Springer Science+Business Media Dordrecht
Subject
Philosophy; Philosophy of Biology; Evolutionary Biology
ISSN
0001-5342
eISSN
1572-8358
DOI
10.1007/s10441-016-9294-z
pmid
27770317
Publisher site
See Article on Publisher Site

Abstract

This article is devoted to the characterization of the basin of attraction of pattern solutions for some slow–fast reaction–diffusion systems with a symmetric property and an underlying oscillatory reaction part. We characterize some subsets of initial conditions that prevent the dynamical system to evolve asymptotically toward solutions which are homogeneous in space. We also perform numerical simulations that illustrate theoretical results and give rise to symmetric and non-symmetric pattern solutions. We obtain these last solutions by choosing particular random initial conditions.

Journal

Acta BiotheoreticaSpringer Journals

Published: Oct 21, 2016

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