TARGET PATTERNS AND SPIRAL WAVES IN REACTION-DIFFUSION SYSTEMS WITH LIMIT CYCLE KINETICSAND WEAK DIFFUSION

In this paper, we study periodic waves in reaction-diffusion systems with limit cycle kinetics and weak diffusion. The results are based on the analysis of a nonlinear partial differential equation which is derived from singular perturbation techniques. We obtain the first order approximation expression of the dispersion curve for periodic wave trains and then show that in the generic case of limit cycle kinetics there is a one parameter family of target patterns and the rotating spiral waves of Archimedian type exist. Finally, we apply these results to the general λ-ω systems.