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 Ca[Image: see text] oscillations and, for the first time, of the Oregonator model. We achieve simulations with up to [Image: see text] 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.