Partially integrable dynamics of hierarchical populations of coupled oscillators

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.

4 pages, 1 figure

References in corpus (2)

• Low Dimensional Behavior of Large Systems of Globally Coupled Oscillators
• Synchronization in networks of networks: the onset of coherent collective behavior in systems of interacting populations of heterogeneous oscillators

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