Abstract: We consider a system of stochastic reaction-diffusion equations for two species with a multiplicative noise term which is given by an infinite-dimensional Wiener process with covariance operator $Q$. In our case, the reaction function describes a competition behaviour between the species, i.e. they compete for the food and environmental resources in the considered bounded domain.
We use a variational approach to show the existence of solutions for this competition model. Moreover, we review existing results for the long-time behaviour in the deterministic setting and compare these solutions with our numerical simulations of the stochastic model in 2D. Therefore, we employ a finite element discretisation with semi-implicit Euler-Maruyama time stepping.