Partially integrable dynamics of hierarchical populations of coupled oscillators

TL;DR

This paper develops a reduction method for hierarchical oscillator populations with heterogeneous coupling, enabling analysis of complex dynamics including novel quasiperiodic chimera states.

Contribution

It introduces a reduction approach based on the Watanabe-Strogatz ansatz for heterogeneous populations, applicable in the thermodynamic limit, and demonstrates its use on the Kuramoto model.

Findings

Reduction simplifies analysis of large oscillator ensembles.

Discovery of a novel quasiperiodic chimera state.

Applicable to various subpopulation configurations.

Abstract

We consider oscillator ensembles consisting of subpopulations of identical units, with a general heterogeneous coupling between subpopulations. Using the Watanabe-Strogatz ansatz we reduce the dynamics of the ensemble to a relatively small number of dynamical variables plus constants of motion. This reduction is independent of the sizes of subpopulations and remains valid in the thermodynamic limits. The theory is applied to the standard Kuramoto model and to the description of two interacting subpopulations, where we report a novel, quasiperiodic chimera state.