Theory of spike spiral waves in a reaction-diffusion system

C. B. Muratov, V. V. Osipov

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

We discovered a type of spiral wave solutions in reaction-diffusion systems—spike spiral wave, which significantly differs from the spiral waves observed in the models of FitzHugh-Nagumo type. We present an asymptotic theory of these waves in the Gray-Scott model [Chem. Sci. Eng. 38, 29 (1983)]. We derive the kinematic relations describing the shape of this spiral, and find the dependence of its main parameters on the control parameters. The theory does not rely on the specific features of the Gray-Scott model and thus is expected to be applicable to a broad range of reaction-diffusion systems.

Original languageEnglish (US)
Pages (from-to)242-246
Number of pages5
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume60
Issue number1
DOIs
StatePublished - 1999
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

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