Pattern formation induced by additive noise: a moment-based analysis
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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.
KeywordsSpectroscopy Neural Network State Physics Crucial Role Complex System
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