Low-dimensional dynamics of phase oscillators driven by Cauchy noise

TL;DR

This paper extends the understanding of phase oscillator systems by demonstrating that low-dimensional dynamics persist under Cauchy noise, aligning with numerical simulations and linking identical and heterogeneous oscillators.

Contribution

It introduces a novel analysis of low-dimensional dynamics in phase oscillators driven by Cauchy noise, bridging noise-driven and natural frequency heterogeneity cases.

Findings

Low-dimensional dynamics match numerical simulations.

Identical oscillators with Cauchy noise behave like heterogeneous ones.

The approach simplifies studying noise-driven systems via natural frequency heterogeneity.

Abstract

Phase oscillator systems with global sine-coupling are known to exhibit low-dimensional dynamics. In this paper, such characteristics are extended to phase oscillator systems driven by Cauchy noise. The low-dimensional dynamics solution agreed well with the numerical simulations of noise-driven phase oscillators in the present study. The low-dimensional dynamics of identical oscillators with Cauchy noise coincided with those of heterogeneous oscillators with Cauchy-distributed natural frequencies. This allows for the study of noise-driven identical oscillator systems through heterogeneous oscillators without noise and vice versa.