Analytical Approach to Noise Effects on Synchronization in a System of Coupled Excitable Elements

TL;DR

This paper presents an analytical method using the nonlinear Fokker-Planck equation to study how noise and constant currents influence synchronization in coupled excitable elements, revealing bifurcation similarities.

Contribution

It introduces a deterministic nonlinear dynamics approach to analyze noise effects in coupled excitable systems without approximations.

Findings

Noise and constant currents induce oscillations via subcritical Hopf bifurcations.

The system exhibits similar bifurcation behavior with and without noise.

Analytical results align with known dynamical phenomena in excitable systems.

Abstract

We report relationships between the effects of noise and applied constant currents on the behavior of a system of excitable elements. The analytical approach based on the nonlinear Fokker-Planck equation of a mean-field model allows us to study the effects of noise without approximations only by dealing with deterministic nonlinear dynamics . We find the similarity, with respect to the occurrence of oscillations involving subcritical Hopf bifurcations, between the systems of an excitable element with applied constant currents and mean-field coupled excitable elements with noise.