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Approximate solution to the stochastic Kuramoto model
Citation key Sonnenschein2013c
Author Sonnenschein, B., and Schimansky-Geier, L.
Pages 052111
Year 2013
DOI 10.1103/PhysRevE.88.052111
Journal Phys. Rev. E
Volume 88
Number 5
Month November
Publisher American Physical Society
Abstract 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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