Chemical Waves and Chemical Turbulence

Abstract

The purpose of this talk is to present a unified viewpoint about the pattern formation in an oscillating reaction-diffusion system. A general equation describing it, is:

$$\mathop X\limits^. = R(X) + D\Delta ^2 X$$

(1) Here X is a vector composed of concentration variables, R(X) represents the reaction part, and D is a diagonal diffusion matrix. Without going into the details of the properties of the subsystem $\mathop X\limits^. = R(X)$, we assume here simply that this subsystem has a stable time-periodic solution X_O(t) of limit cycle type. Thus we are concerned with the pattern formation taking place in a system composed of many local nonlinear oscillators coupled with each other through diffusion.