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An approximate solution to the stochastic Kuramoto model
Citation key Sonnenschein2013a0
Author Sonnenschein, B., and Schimansky-Geier, L.
Year 2013
Month August
Abstract We study Kuramoto phase oscillators with temporal fluctations in the frequencies. The infinite-dimensional system can be reduced in 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 new tight upper bound for the corresponding scaling.
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