Phase velocity and phase diffusion in periodically driven discrete state systems

TL;DR

This paper develops a theoretical framework to analyze phase velocity and diffusion in periodically driven two-state stochastic systems, demonstrating phase synchronization and validating results with simulations of excitable systems.

Contribution

Introduces an analytical theory for phase dynamics in driven two-state stochastic models, including non-Markovian systems, with explicit formulas and validation.

Findings

Explicit formulas for phase velocity and diffusion coefficient

Demonstrates stochastic synchronization with periodic driving

Good agreement with FitzHugh-Nagumo system simulations

Abstract

We develop a theory to calculate the effective phase diffusion coefficient and the mean phase velocity in periodically driven stochastic models with two discrete states. This theory is applied to a dichotomically driven Markovian two state system. Explicit expressions for the mean phase velocity, the effective phase diffusion coefficient and the P\'eclet number are analytically calculated. The latter shows as a measure of phase-coherence forced synchronization of the stochastic system with respect to the periodic driving. In a second step the theory is applied to a non Markovian two state model modeling excitable systems. The results prove again stochastic synchronization to the periodic driving and are in good agreement with simulations of a stochastic FitzHugh-Nagumo system.