Partially Integrable Dynamics of Populations of Nonidentical Oscillators with Global Nonlinear Coupling

COFFEE_KLATCH · Invited

Abstract

We consider ensembles of sine-coupled phase oscillators 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 microscopic constants of motion. This reduction is independent of the sizes of subpopulations and remains valid in the thermodynamic limits, where these sizes or/and the number of subpopulations are infinite. We demonstrate that the approach to the dynamics of such systems, recently proposed by Ott and Antonsen, corresponds to a particular choice of microscopic constants of motion. The theory is applied to the standard Kuramoto model and to the description of two interacting subpopulations, exhibiting a chimera state. Furthermore, we analyze the dynamics of the extension of the Kuramoto model for the case of nonlinear coupling and demonstrate the multistability of synchronous states.

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Authors

  • Kurt Wiesenfeld

    Miami University, Summa Health System, Akron, John Carroll University, Prof, Dr, BfS, Germany, Florida State University, Monmouth College, Ohio Wesleyan University, Kenyon College, University of Cincinnati, Brookhaven National Lab, University of Wisconsin Oshkosh, Dept. of Chermical Engineering, Carnegie Mellon University, Cleveland State University, The Neurological Institute, Epilepsy Center, Department of Neurology, Cleveland Clinic, Un. of Stockholm, The University of Akron, Case Western Reserve University, West Virginia University, Kalamazoo College and Editor, American Journal of Physics, Denison University, University of Southern Florida, Johannes-Gutenberg-Universitat, BfS (Germany), Shanghai Jiao Tong University, Department of Physics, West Virginia University, Kansas State University, The Pennsylvania State University, University of Wisconsin-Oshkosh, Purdue University, Saint Jospeh's College, University of Washington, Indiana University, University of Potsdam, Georgia Institute of Technology