Stochastic Simulations of Pattern Formation in Excitable Media

We present a method for mesoscopic, dynamic Monte Carlo simulations of pattern formation in excitable reaction-diffusion systems. Using a two-level parallelization approach, our simulations cover the whole range of the parameter space, from the noise-dominated low-particle number regime to the quasi-deterministic high-particle number limit. Three qualitatively different case studies are performed that stand exemplary for the wide variety of excitable systems. We present mesoscopic stochastic simulations of the Gray-Scott model, of a simplified model for intracellular Ca2+ oscillations and, for the first time, of the Oregonator model. We achieve simulations with up to 10(10) particles. The software and the model files are freely available and researchers can use the models to reproduce our results or adapt and refine them for further exploration.