View AbstractAbstract: Reaction and diffusion of chemical species can produce a variety of patterns, reminiscent of those often seen in nature. The Gray Scott system is a coupled equation of reaction diffusion type, modelling these kind of patterns. Depending on the parameter, stripes, waves, cloud streets, or sand ripples may appear.
These systems are the macroscopic model of microscopic dynamics.
Here, in the derivation of the equation the random fluctuation of the molecules are neglected.
Adding a stochastic noise, the inherit randomness
of the microscopic behaviour is modelled. In particular, we add a time homogenous spatial Gaussian random field with given spectral measure.
In the talk we present our main result about the stochastic Gray Scott system.
In addition, we introduce and explain an algorithm for its numerical approximation by a Operator splitting method. Finally we present some examples illustrating the dynamical behaviour of the stochastic Gray Scott system.