Wave nucleation rate in excitable systems in the low noise limit

TL;DR

This paper investigates how random fluctuations induce wave nucleation in excitable systems, using a stochastic Fitzhugh-Nagumo model to analyze the most probable escape paths and nucleation rates.

Contribution

It introduces a method to compute wave nucleation rates in excitable media driven by noise, applicable to biological and non-equilibrium systems.

Findings

Determined nucleation rates via action minimization.

Identified most probable escape paths for wave formation.

Provided a framework for studying nucleation in non-potential systems.

Abstract

Motivated by recent experiments on intracellular calcium dynamics, we study the general issue of fluctuation-induced nucleation of waves in excitable media. We utilize a stochastic Fitzhugh-Nagumo model for this study, a spatially-extended non-potential pair of equations driven by thermal (i.e. white) noise. The nucleation rate is determined by finding the most probable escape path via minimization of an action related to the deviation of the fields from their deterministic trajectories. Our results pave the way both for studies of more realistic models of calcium dynamics as well as of nucleation phenomena in other non-equilibrium pattern-forming processes.