Pattern formation in reacting and diffusing systems

Abstract

A mechanism is described, whereby stable sharply differentiated (dissipative) structures can evolve naturally within a mixture of reacting and diffusing substances. Our model has two reacting components, with one diffusion coefficient much smaller than the other. Unlike patterned states obtained by small amplitude analysis near uniform states, our structures have large amplitude and serve to divide the reactor into subregions, each corresponding to a distinct phase for the system. The evolution of the structured stationary state from an arbitrary initial distribution occurs in two stages. The first involves differentiation into subregions, and the second involves the migration of the boundaries of the subregions into a stable final configuration. A singular perturbation analysis and the theory of motion of wavefronts is used to deduce these qualitative properties.