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We consider the Kuramoto model of an ensemble of interacting oscillatorsallowing 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 empiricalstability conditions which, for the case of incoherence, become exact. Inaddition to making new theoretical predictions, we show that many earlierresults follow naturally from our general framework. The results are applicablein scientific contexts ranging from physics to biology.

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