JournalsifbVol. 20, No. 2pp. 297–336

A multiple scale pattern formation cascade in reaction-diffusion systems of activator-inhibitor type

  • Marie Henry

    Université d’Aix-Marseille, Marseille, France
  • Danielle Hilhorst

    Université Paris-Sud, Orsay, France
  • Cyrill B. Muratov

    New Jersey Institute of Technology, Newark, USA
A multiple scale pattern formation cascade in reaction-diffusion systems of activator-inhibitor type cover
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Abstract

A family of singular limits of reaction-diffusion systems of activator-inhibitor type in which stable stationary sharp-interface patterns may form is investigated. For concreteness, the analysis is performed for the FitzHugh-Nagumo model on a suitably rescaled bounded domain in RN\mathbb R^N, with N2N \geq 2. It is shown that when the system is sufficiently close to the limit the dynamics starting from the appropriate smooth initial data breaks down into five distinct stages on well-separated time scales, each of which can be approximated by a suitable reduced problem. The analysis allows to follow fully the progressive refinement of spatio-temporal patterns forming in the systems under consideration and provides a framework for understanding the pattern formation scenarios in a large class of physical, chemical, and biological systems modeled by the considered class of reaction-diffusion equations.

Cite this article

Marie Henry, Danielle Hilhorst, Cyrill B. Muratov, A multiple scale pattern formation cascade in reaction-diffusion systems of activator-inhibitor type. Interfaces Free Bound. 20 (2018), no. 2, pp. 297–336

DOI 10.4171/IFB/403