On the Formation of Dissipative Structures in Reaction-Diffusion Systems: Reductive Perturbation Approach

Abstract

A unified viewpoint on the dynamics of spatio-temporal organization in various reaction-diffusion systems is presented. A dynamical similarity law attained near the instability points plays a decisive role in our whole theory. The method of reductive perturbation is used for extracting a scale-invariant part from original macroscopic equations of motion. It is shown that in many cases the dynamics near the instability point is governed by the time-dependent Ginzburg-Landau equation with coefficients which are in general complex numbers. An important effect of the imaginary parts of these coefficients on the stability of a spatially uniform limit cycle against inhomogeneous perturbation is also discussed.