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arXiv · 0906.2124

Spontaneous synchronization of coupled oscillator systems with frequency adaptation

Dane Taylor·Edward Ott·Juan G. Restrepo
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Abstract

We study the synchronization of Kuramoto oscillators with all-to-all coupling in the presence of slow, noisy frequency adaptation. In this paper we develop a new model for oscillators which adapt both their phases and frequencies. It is found that this model naturally reproduces some observed phenomena that are not qualitatively produced by the standard Kuramoto model, such as long waiting times before the synchronization of clapping audiences. By assuming a self-consistent steady state solution, we find three stability regimes for the coupling constant k, separated by critical points k1 and k2: (i) for k k2, the incoherent state becomes unstable and only the synchronized state exists; (iii) for k1 k2), the average waiting time grows logarithmically with the number of oscillators.

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Dane Taylor, Edward Ott, Juan G. Restrepo. 2009-06-11. Spontaneous synchronization of coupled oscillator systems with frequency adaptation. https://doi.org/10.1103/physreve.81.046214

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