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

Marie Henry, Danielle Hilhorst, Cyrill B. Muratov

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)297-336
Number of pages40
JournalInterfaces and Free Boundaries
Volume20
Issue number2
DOIs
StatePublished - 2018

All Science Journal Classification (ASJC) codes

  • Surfaces and Interfaces

Keywords

  • Multiscale analysis
  • Nonlinear dynamics
  • Pattern formation
  • Singular perturbations

Fingerprint

Dive into the research topics of 'A multiple scale pattern formation cascade in reaction-diffusion systems of activator-inhibitor type'. Together they form a unique fingerprint.

Cite this