Phase velocity and phase diffusion in periodically driven discrete state systems

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 Péclet 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.

11 pages, 7 figures

References in corpus (5)

• Statistics of transition times, phase diffusion and synchronization in periodically driven bistable systems
• Rate description of Fokker-Planck processes with time dependent parameters
• Coupled three-state oscillators
• Theory of frequency and phase synchronization in a rocked bistable stochastic system
• Stochastic resonance in a non Markovian discrete state model for excitable systems

Cited by in corpus (4)

• Noise induced forced synchronization of global variables in coupled bistable systems
• The role of fluctuations in the response of coupled bistable units to weak driving time-periodic forces
• Drift and Diffusion in Periodically Driven Renewal Processes
• Synchronization of weakly perturbed Markov chain oscillators