Synchronization of Stochastically Coupled Oscillators: Dynamical Phase Transitions and Large Deviations Theory (or Birds and Frogs)

COFFEE_KLATCH · Invited

Abstract

Systems of oscillators coupled non-linearly (stochastically or not) are ubiquitous in nature and can explain many complex phenomena: coupled Josephson junction arrays, cardiac pacemaker cells, swarms or flocks of insects and birds, etc. They are know to have a non-trivial phase diagram, which includes chaotic, partially synchronized, and fully synchronized phases. A traditional model for this class of problems is the Kuramoto system of oscillators, which has been studied extensively for the last three decades. The model is a canonical example for non-equilibrium, dynamical phase transitions, so little understood in physics. From a stochastic analysis point of view, the transition is described by the large deviations principle, which offers little information on the scaling behavior near the critical point. I will discuss a special case of the model, which allows a rigorous analysis of the critical properties of the model, and reveals a new, anomalous scaling behavior in the vicinity of the critical point.

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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