Giant Amplification of Noise in Fluctuation-Induced Pattern Formation

Abstract

The amplitude of fluctuation-induced patterns might be expected to be proportional to the strength of the driving noise, suggesting that such patterns would be difficult to observe in nature. Here, we show that a large class of spatially extended dynamical systems driven by intrinsic noise can exhibit giant amplification, yielding patterns whose amplitude is comparable to that of deterministic Turing instabilities. The giant amplification results from the interplay between noise and nonorthogonal eigenvectors of the linear stability matrix, yielding transients that grow with time, and which, when driven by the ever-present intrinsic noise, lead to persistent large amplitude patterns. This mechanism shows that fluctuation-induced Turing patterns are observable, and are not strongly limited by the amplitude of demographic stochasticity nor by the value of the diffusion coefficients.