Simulation Analysis of the Influence of Random Disturbances on Shell Pattern Formations

In the natural world, many spatio-temporal patterns are observed. In this paper, we take up the pattern formation processes of shell patterns on Amoria ellioti and Conus marmoreus among spatio-temporal patterns. As the mathematical model to generate the patterns, some sorts of reaction-diffusion equations have been proposed by many researchers in a deterministic situation, however, in this paper, taking the disturbance into consideration, we propose the stochastic reaction diffusion equation as the model to generate shell patterns and study the influence of the disturbance on the pattern formation by the numerical simulation.