Dynamics of multi-frequency oscillator ensembles with resonant coupling

TL;DR

This paper investigates the complex synchronization behaviors in populations of resonantly coupled oscillators with different frequencies, deriving a phase model and analyzing various collective states.

Contribution

It introduces a Kuramoto-type phase model for resonantly coupled oscillator populations with 2:1 frequency relation, and applies the Watanabe-Strogatz approach for theoretical analysis.

Findings

Ensembles can exhibit full synchrony, partial synchrony, or asynchrony.

The model captures diverse collective dynamics depending on coupling parameters.

Theoretical framework explains observed synchronization patterns.

Abstract

We study dynamics of populations of resonantly coupled oscillators having different frequencies. Starting from the coupled van der Pol equations we derive the Kuramoto-type phase model for the situation, where the natural frequencies of two interacting subpopulations are in relation 2:1. Depending on the parameter of coupling, ensembles can demonstrate fully synchronous clusters, partial synchrony (only one subpopulation synchronizes), or asynchrony in both subpopulations. Theoretical description of the dynamics based on the Watanabe-Strogatz approach is developed.