Spontaneous synchronization of coupled oscillator systems with frequency adaptation

Details Spontaneous synchronization of coupled oscillator systems with frequency adaptation Spontaneous synchronization of coupled oscillator systems with frequency adaptation

2009-06-11

arxiv.org/abs/0906.2124v2

Physics

Condensed Matter

Statistical Mechanics

8 page Tex file, 6 figures

Scientific paper

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 kk2, the incoherent state becomes unstable and only the synchronized state exists; (iii) for k1k2), the average waiting time grows logarithmically with the number of oscillators.

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