Acta Biotheoretica

, Volume 64, Issue 4, pp 311–325 | Cite as

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

Regular Article
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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.

Keywords

Reaction diffusion systems Slow–fast analysis Limit-cycles Pattern formation FitzHugh–Nagumo 

Notes

Acknowledgments

Some part of this research has been done during the visiting period of the first author at CIMS, NYU in 2014–2015. He would like to thank L. Mertz, as some interesting discussions during this period, became concrete in this paper. The authors would like to thank Région Haute Normandie and—FEDER (RISC project) for financial support.

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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.UNIHAVRE, LMAH, FR-CNRS-3335, ISCNNormandie UnivLe HavreFrance

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