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Stationary and Traveling Wave States of the Kuramoto Model with an Arbitrary Distribution of Frequencies and Coupling Strengths

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Article number064101
<mark>Journal publication date</mark>5/02/2013
<mark>Journal</mark>Physical review letters
Issue number6
Number of pages5
Publication statusPublished
Original languageEnglish


We consider the Kuramoto model of an ensemble of interacting oscillators allowing for an arbitrary distribution of frequencies and coupling strengths. We define a family of traveling wave states as stationary in a rotating frame, and derive general equations for their parameters. We suggest empirical stability conditions which, for the case of incoherence, become exact. In addition to making new theoretical predictions, we show that many earlier results follow naturally from our general framework. The results are applicable in scientific contexts ranging from physics to biology. DOI: 10.1103/PhysRevLett.110.064101