Geodesic
A multiple scale pattern formation cascade in reaction-diffusion systems of activator-inhibitor type
Marie Henry1 ; Danielle Hilhorst2 ; Cyrill B. Muratov3
1Université d’Aix-Marseille, Marseille, France
2Université Paris-Sud, Orsay, France
3New Jersey Institute of Technology, Newark, USA
Interfaces and free boundaries, Tome 20 (2018) no. 2, pp. 297-336

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DOI

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 reaction-diffusion equations.
DOI : 10.4171/ifb/403
Classification : 35-XX
Mots-clés : Pattern formation, multiscale analysis, singular perturbations, nonlinear dynamics

Marie Henry  1   ; Danielle Hilhorst  2   ; Cyrill B. Muratov  3

1 Université d’Aix-Marseille, Marseille, France
2 Université Paris-Sud, Orsay, France
3 New Jersey Institute of Technology, Newark, USA 
Marie Henry; Danielle Hilhorst; Cyrill B. Muratov. A multiple scale pattern formation cascade in reaction-diffusion systems of activator-inhibitor type. Interfaces and free boundaries, Tome 20 (2018) no. 2, pp. 297-336. doi: 10.4171/ifb/403
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