Pattern formation induced by additive noise: a moment-based analysis

We analyze the condition for instability and pattern formation induced by additive noise in spatially extended systems. The approach is based on consideration of higher moments which extract out nonlinearities of appropriate order. Our analysis reveals that cubic nonlinearity plays a crucial role for the additive noise to a leading order that determines the instability threshold which is corroborated by numerical simulation in two specific reaction-diffusion systems. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2005