Theory of Spike Spiral Waves in a Reaction-Diffusion System

Details Theory of Spike Spiral Waves in a Reaction-Diffusion System Theory of Spike Spiral Waves in a Reaction-Diffusion System

1998-08-11

arxiv.org/abs/patt-sol/9808004v1

Phys Rev. E 60, 242 (1999).

Nonlinear Sciences

Pattern Formation and Solitons

4 pages (REVTeX), 2 figures (postscript), submitted to Phys. Rev. Lett

Scientific paper

10.1103/PhysRevE.60.242

We discovered a new type of spiral wave solutions in reaction-diffusion systems --- spike spiral wave, which significantly differs from spiral waves observed in FitzHugh-Nagumo-type models. We present an asymptotic theory of these waves in Gray-Scott model. 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 Gray-Scott model and thus is expected to be applicable to a broad range of reaction-diffusion systems.

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