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 obser ved in the models of FitzHugh-Nagumo type. We present an asymptotic theory of these waves in the Gray-Scott model [Chem. Sci. Erig. 38, 29 (1983)]. We derive the kinematic relations describing the shape of this spiral, and fi nd the dependence of its main parameters on the control parameters. The the ory 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 system s. [S1063-651X(99)09507-0].