Stochastic sensitivity analysis of stationary patterns in spatially extended systems

Abstract

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.

Analytical modeling of the approximate solution behavior of multi‐dimensional reaction–diffusion Brusselator system

“…Time‐dependent coupled partial differential equations (PDEs) play a crucial role in modeling various chemical and biological processes 1–12 . The coupled Brusselator model is one such nonlinear coupled PDE that seeks applications in cooperative processes of chemical kinetics or biochemical reactions 13 .…”

“…Time-dependent coupled partial differential equations (PDEs) play a crucial role in modeling various chemical and biological processes. [1][2][3][4][5][6][7][8][9][10][11][12] The coupled Brusselator model is one such nonlinear coupled PDE that seeks applications in cooperative processes of chemical kinetics or biochemical reactions. 13 For example, in the patterns formation on animal skins with and without cross-diffusion, in the creation of ozone by atomic oxygen through a triple collision, in enzymatic reactions, in plasma and laser physics.…”