Effective phase dynamics of noise-induced oscillations in excitable systems

TL;DR

This paper develops a deterministic phase dynamics framework to accurately describe noise-induced oscillations in excitable systems, providing analytical and data-driven methods for complex scenarios and applications to forced oscillations.

Contribution

It introduces a novel effective phase equation that captures the frequency and distribution of noise-induced oscillations, including analytical solutions and data processing techniques.

Findings

Effective phase equation accurately describes noise-induced oscillations.

Analytical solution obtained for one-dimensional systems.

Method demonstrated on periodically forced noise-induced oscillations.

Abstract

We develop an effective description of noise-induced oscillations based on deterministic phase dynamics. The phase equation is constructed to exhibit correct frequency and distribution density of noise-induced oscillations. In the simplest one-dimensional case the effective phase equation is obtained analytically, whereas for more complex situations a simple method of data processing is suggested. As an application an effective coupling function is constructed that quantitatively describes periodically forced noise-induced oscillations.