Analysis of stochastic sensitivity of Turing patterns in distributed reaction–diffusion systems

In this paper, a distributed stochastic Brusselator model with diffusion is studied. We show that a variety of stable spatially heterogeneous patterns is generated in the Turing instability zone. The effect of random noise on the stochastic dynamics near these patterns is analysed by direct numerical simulation. Noise-induced transitions between coexisting patterns are studied. A stochastic sensitivity of the pattern is quantified as the mean-square deviation from the initial unforced pattern. We show that the stochastic sensitivity is spatially non-homogeneous and significantly differs for coexisting patterns. A dependence of the stochastic sensitivity on the variation of diffusion coefficients and intensity of noise is discussed.