Spatial pattern formation in external noise: theory and simulation.

Spatial pattern formation in fluctuating media is researched analytically from the point of view of the order parameters concept. A reaction-diffusion system with external noise is considered as a model of such media. Stochastic equations for unstable mode amplitudes (order parameters), the dispersion equation for averaged amplitudes of unstable modes, and the Fokker-Planck equation for the order parameters are obtained. The theory developed makes it possible to analyze different noise-induced effects including the variation of boundaries of ordering and disordering phase transitions depending on the parameters of external noise.