Institute of Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Straße 24-25, 14476 Potsdam, Germany.
Department of Control Theory, Nizhny Novgorod State University, Gagarin Av. 23, 606950, Nizhny Novgorod, Russia.
Phys Rev E. 2019 Sep;100(3-1):032210. doi: 10.1103/PhysRevE.100.032210.
Supercritical Kuramoto oscillators with distributed frequencies can be separated into two disjoint groups: an ordered one locked to the mean field, and a disordered one consisting of effectively decoupled oscillators-at least so in the thermodynamic limit. In finite ensembles, in contrast, such clear separation fails: The mean field fluctuates due to finite-size effects and thereby induces order in the disordered group. This publication demonstrates this effect, similar to noise-induced synchronization, in a purely deterministic system. We start by modeling the situation as a stationary mean field with additional white noise acting on a pair of unlocked Kuramoto oscillators. An analytical expression shows that the cross-correlation between the two increases with decreasing ratio of natural frequency difference and noise intensity. In a deterministic finite Kuramoto model, the strength of the mean-field fluctuations is inextricably linked to the typical natural frequency difference. Therefore, we let a fluctuating mean field, generated by a finite ensemble of active oscillators, act on pairs of passive oscillators with a microscopic natural frequency difference between which we then measure the cross-correlation, at both super- and subcritical coupling.
具有分布式频率的超临界 Kuramoto 振荡器可以分为两个不相交的组：一个有序的组被锁定到平均场，另一个无序的组由有效解耦的振荡器组成——至少在热力学极限下是这样。相比之下，在有限的集合中，这种清晰的分离是失败的：由于有限尺寸效应，平均场会发生波动，从而在无序组中引起有序。本出版物在一个纯粹的确定性系统中展示了这种类似于噪声诱导同步的效果。我们首先将这种情况建模为一个带有附加白噪声的静止平均场，作用于一对未锁定的 Kuramoto 振荡器上。一个解析表达式表明，两个振荡器之间的互相关随着自然频率差和噪声强度比的减小而增加。在确定性有限 Kuramoto 模型中，平均场波动的强度与典型的自然频率差密不可分。因此，我们让一个由活跃振荡器的有限集合产生的波动平均场作用于一对具有微观自然频率差的被动振荡器上，然后在超临界和亚临界耦合下测量它们之间的互相关。
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