Spatial Pattern Formation in External Noise: Theory and Simulation
Svetlana E. Kurushina, Valery V. Maximov, Yuri M. Romanovskii
TL;DR
This paper develops a theoretical framework for understanding how external noise influences spatial pattern formation in excitable media, using reaction-diffusion models and stochastic equations to analyze noise-induced effects.
Contribution
It introduces a novel analytical approach based on order parameters and stochastic equations to study noise-induced pattern formation in reaction-diffusion systems.
Findings
Derived stochastic equations for unstable mode amplitudes
Formulated dispersion equations for average amplitudes
Analyzed noise-dependent phase transition boundaries
Abstract
Spatial pattern formation in excitable fluctuating media was researched analytically from the point of view of the order parameters concept. The reaction-diffusion system in external noise is considered as a model of such medium. Stochastic equations for the unstable mode amplitudes (order parameters), dispersion equations for the unstable mode averaged amplitudes, and the Fokker-Planck equation for the order parameters have been obtained. The developed theory 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
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