Analysis of Turing patterns by stochastic reaction diffusion systems

Abstract

This paper is concerned with the mathematical modeling of Turing pattern formations by stochastic reaction diffusion equations. First, by introducing the stochastic reaction diffusion equations, a mathematical model of pattern formation is proposed. Secondly, the existence theorem of the unique solution of the proposed equation is established. Finally, analysis of the process of pattern formation is performed through simulation experiments and the influence of the disturbance on pattern formation is studied as well.