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Approximate solution to the stochastic Kuramoto model
Zitatschlüssel Sonnenschein2013c
Autor Sonnenschein, B., and Schimansky-Geier, L.
Seiten 052111
Jahr 2013
DOI 10.1103/PhysRevE.88.052111
Journal Phys. Rev. E
Jahrgang 88
Nummer 5
Monat November
Verlag American Physical Society
Zusammenfassung We study Kuramoto phase oscillators with temporal fluctuations in the frequencies. The infinite-dimensional system can be reduced in a Gaussian approximation to two first-order differential equations. This yields a solution for the time-dependent order parameter, which characterizes the synchronization between the oscillators. The known critical coupling strength is exactly recovered by the Gaussian theory. Extensive numerical experiments further show that the analytical results are very accurate below and sufficiently above the critical value. We obtain the asymptotic order parameter in closed form, which suggests a tighter upper bound for the corresponding scaling. As a last point, we elaborate the Gaussian approximation in complex networks with distributed degrees.
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