Microscopic model for FitzHugh-Nagumo dynamics

Publication Type:

Journal Article

Authors:

Source:

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Volume 55, Number 5, p.5657-5670 (1997)

URL:

https://www.scopus.com/inward/record.uri?eid=2-s2.0-0031146972&doi=10.1103%2fPhysRevE.55.5657&partnerID=40&md5=dd3031edd03995426bd9618f205c6446

Keywords:

Bifurcation (mathematics), Birth death processes, Brownian movement, Computer Simulation, Diffusion, FitzHugh-Nagumo dynamics, Markov processes, Mass action rate law, Mathematical models, Phase transitions, Probability, Reaction kinetics

Abstract:

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. © 1997 The American Physical Society.