The Kuramoto Model with Time-Varying Parameters

TL;DR

This paper generalizes the Kuramoto model by incorporating time-dependent parameters influenced by external fields, providing a more accurate analysis of the system's dynamics beyond previous adiabatic methods.

Contribution

It introduces a novel framework for analyzing the Kuramoto model with explicit time-varying parameters, capturing external influences on oscillator frequencies and couplings.

Findings

The model accounts for external, time-dependent influences on oscillators.

It offers a faithful description of the system's overall dynamics.

Previous adiabatic approaches are insufficient for this scenario.

Abstract

We introduce a generalization of the Kuramoto model by explicit consideration of time-dependent parameters. The oscillators' natural frequencies and/or couplings are supposed to be influenced by external, time-dependant fields, with constant or randomly-distributed strengths. As a result, the dynamics of an external system is being imposed on top of the autonomous one, a scenario that cannot be treated adequately by previous (adiabatic) approaches. We now propose an analysis which describes faithfully the overall dynamics of the system.