Turing pattern formation in the brusselator model with superdiffusion

A. A. Golovin, Bernard J Matkowsky, Vladimir Volpert

Research output: Contribution to journalArticle

59 Scopus citations

Abstract

The effect of superdiffusion on pattern formation and pattern selection in the Brus-selator model is studied. Our linear stability analysis shows, in particular, that, unlike the case of normal diffusion, the Turing instability can occur even when diffusion of the inhibitor is slower than that of the initiator. A weakly nonlinear analysis yields a system of amplitude equations, analysis of which predicts parameter regimes where hexagons, stripes, and their coexistence are expected. Numerical computations of the original Brusselator model near the stability boundaries confirm the results of the analysis. In addition, further from the stability boundaries, we find a regime of self-replicating spots.

Original languageEnglish (US)
Pages (from-to)251-272
Number of pages22
JournalSIAM Journal on Applied Mathematics
Volume69
Issue number1
DOIs
StatePublished - Nov 6 2008

Keywords

  • Anomalous diffusion
  • Brusselator
  • Pattern formation
  • Superdiffusion
  • Turing instability

ASJC Scopus subject areas

  • Applied Mathematics

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