Microscopic model for FitzHugh-Nagumo dynamics

A microscopic reaction model with a FitzHugh-Nagumo mass action law is introduced. A Markov chain that uses a birth-death description of the reaction mechanism and a random walk model for diffusion is constructed and implemented as a lattice-gas automaton. It is shown that the local particle density probability distribution is binomial in the high diffusion limit and the average particle density is governed by the FitzHugh-Nagumo reaction-diffusion equation. The lattice-gas simulations are able to reproduce phenomena such as labyrinthine patterns and Bloch fronts predicted to exist on the basis of the reaction-diffusion equation. The effects of fluctuations on these chemical patterns, the breakdown of the mass-action and reaction-diffusion descriptions, and the existence of phase transitions in the strong reaction limit are discussed.