Isochronal Phase Reduction and Speed Correction of a Pulse in a Stochastic Kinematic Model

TL;DR

This paper introduces a novel method to compute the stochastic wave speed of pulses in kinematic models with small noise, based on isochronal phase reduction, applicable to excitable media like the FitzHugh-Nagumo system.

Contribution

It provides a new approach for deriving an effective stochastic process for pulse position, enabling efficient and accurate wave speed computation in noisy excitable systems.

Findings

The method accurately predicts wave speed under stochastic forcing.

Numerical demonstrations confirm efficiency and precision.

Applicable to models derived as singular limits of excitable media.

Abstract

We develop a method for computing the stochastic wave speed of pulse solutions in kinematic equations subject to small stochastic forcing based on the isochronal phase reduction. These kinematic equations arise as the singular limit of sharp pulse solutions in the FitzHugh-Nagumo system, and our approach contributes a new perspective and method to the growing body of work on stochastic wave propagation in excitable media. The method yields an effective It\^o process for the wave's position. The coefficients of the It\^o process can be computed deterministically allowing for efficient computation. We demonstrate the efficiency and accuracy of our method through numerical demonstrations.