Introduction

Mathematically, a reaction-diffusion system is obtained by adding some diffusion terms to a set of ordinary differential equations which are first order in time. The reaction-diffusion model is literally an appropriate model for studying the dynamics of chemically reacting and diffusing systems. Actually, the scope of this model is much wider. For instance, in the field of biology, the propagation of the action potential in nerves and nervelike tissues is known to obey this type of equation, and some mathematical ecologists employ reaction-diffusion models for explaining various ecological patterns observed in nature. In some thermodynamic phase transitions, too, the evolution of the local order parameter is governed by reaction-diffusion-type equations if we ignore the fluctuating forces.