Theory of spike spiral waves in a reaction-diffusion system.
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.
Muratov
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Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, New York 10012, USA.
Osipov
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