Sonnenschein Bernard, Schimansky-Geier Lutz
Department of Physics, Humboldt-Universität zu Berlin, Newtonstrasse 15, 12489 Berlin, Germany and Bernstein Center for Computational Neuroscience Berlin, Philippstrasse 13, 10115 Berlin, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Nov;88(5):052111. doi: 10.1103/PhysRevE.88.052111. Epub 2013 Nov 8.
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.
我们研究了频率具有时间波动的Kuramoto相位振子。这个无穷维系统可以在高斯近似下简化为两个一阶微分方程。这就得到了一个随时间变化的序参量的解，该序参量表征了振子之间的同步情况。高斯理论精确地恢复了已知的临界耦合强度。大量的数值实验进一步表明，在临界值以下和足够高于临界值时，解析结果非常准确。我们以封闭形式得到了渐近序参量，这表明了相应标度的更严格上界。最后一点，我们阐述了具有分布度的复杂网络中的高斯近似。
