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

Document Type

Article

Publication Date

1-1-2018

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, with N ≥ 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 reactiondiffusion equations.

Identifier

85049808708 (Scopus)

Publication Title

Interfaces and Free Boundaries

External Full Text Location

https://doi.org/10.4171/IFB/403

ISSN

14639963

First Page

297

Last Page

336

Issue

2

Volume

20

Grant

DMS-0718027

Fund Ref

National Stroke Foundation

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