https://doi.org/10.1140/epjb/e2005-00314-1
Pattern formation induced by additive noise: a moment-based analysis
Indian Association for the Cultivation of Science,
Jadavpur, Kolkata 700 032, India
Corresponding author: a pcdsr@mahendra.iacs.res.in
Received:
7
January
2005
Revised:
26
April
2005
Published online:
11
October
2005
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.
PACS: 82.40.Ck – Pattern formation in reactions with diffusion, flow and heat transfer / 47.54.+r – Pattern selection; pattern formation / 05.45.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 47.20.Ky – Nonlinearity (including bifurcation theory)
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2005
