A Kuramoto coupling of quasi-cycle oscillators

TL;DR

This paper introduces a Kuramoto-type coupling for stochastic quasi-cycle oscillators, demonstrating how increased coupling strength leads to phase synchronization and a critical transition similar to classical Kuramoto models, with implications for neural networks.

Contribution

It extends Kuramoto coupling to quasi-cycle oscillators with noise-driven oscillations, analyzing synchronization transitions and comparing network dynamics.

Findings

Synchronization increases with coupling strength.

A critical coupling value induces abrupt transition to synchronization.

Large networks exhibit a phase transition similar to classical Kuramoto models.

Abstract

A family of stochastic processes has quasi-cycle oscillations if the oscillations are sustained by noise. For such a family we define a Kuramoto-type coupling of both phase and amplitude processes. We find that synchronization, as measured by the phase-locking index, increases with coupling strength, and appears, for larger network sizes, to have a critical value, at which the network moves relatively abruptly from incoherence to complete synchonization as in Kuramoto couplings of fixed amplitude oscillators. We compare several aspects of the dynamics of unsynchronized and highly synchronized networks. Our motivation comes from synchronization in neural networks.