Stochastic sensitivity analysis of stationary patterns in spatially extended systems

In this paper, a spatially extended stochastic reaction-diffusion model is studied. Due to Turing instability, stable nonhomogeneous stationary patterns are generated in such models. A theoretical approach to estimating the mean-square deviation of random solutions from the stable deterministic pattern-attractor is demonstrated. Stochastic sensitivity functions for stable stationary patterns are introduced. Theoretical evaluations are compared with statistically obtained data. Based on this approach, we investigate stochastic properties of different patterns in Brusselator. Variations in pattern sensitivity to noise and phenomenon of stochastic preference are discussed.