Pattern Formation in Oscillatory Chemical Reactions

Abstract

The present paper deals with the problem of pattern formation which takes place in a self-oscillatory continuous medium. Specifically, a mathematically tract­ able two-component field of purely dissipative nature will be considered throughout for primary understanding of some typical wave phenomena of dissipative origin. As an important example of such systems one may mention a two-component reac­ tion-diffusion system driven far from equilibrium, to which a large part of this paper has been devoted. Let a chemically reacting system be represented by a macroscopic dynamical system. Then its fundamental state variables may be taken to be the concen­ trations of reactants. If the concentrations of some species are externally con­ trollable so as to be kept constant in time, or if their time-variation is very slow as compared with the processes of interest, these quantities may be treated as the time-independent parameters that prevent the system from going to thermal equi­ librium. It often occurs that a certain parameter has a threshold value for the appearance of the concentration oscillations of limit-cycle type. 1J Our main concern is the spatia-temporal organization closely connected with this type of oscillation. In particular, we shall discuss in detail that our model system can display some well-known wave phenomena such as the circular and spiral pattern formation observed in a malonic acid-bromate system or analogous reaction systems. 2 l~ 5 l