Rotating Spiral Waves and Oscillations in Reaction-Diffusion Equations

Abstract

This chapter describes the rotating spiral waves and oscillations in reaction–diffusion equations. Rotating spiral waves arise naturally as models of spatially organized activity in various chemical and biochemical processes. The Belousov–Zhabotinsky reaction provides a classic example. Experiments with this reaction in a two-dimensional medium produce spiral concentration patterns that rotate with constant frequency about a fixed center. These waves result from interplay between the chemical process of reaction and the physical process of molecular diffusion. The chapter discusses the existence and various analytical and asymptotic properties of these waves. It presents the concrete computations for specific parameter values. The demonstration of the existence of such rotating spiral waves, which are smooth from the origin to infinity, resolves the important issue. The chapter explores the effect of spatial diffusion on oscillatory states in arbitrary multispecies growth models having hereditary terms.