Wang Yongqiang, Doyle Francis J
Department of Chemical Engineering, University of California, Santa Barbara, California 93106 USA.
Automatica (Oxf). 2011 Jun 1;47(6):1236-1242. doi: 10.1016/j.automatica.2011.01.074.
Synchronization of connected oscillator networks under global and local cues is ubiquitous in both science and engineering. Over the last few decades, enormous attention has been paid to study synchronization conditions of connected oscillators in chemistry, physics, mechanics, and particularly in biology. However, the influences of global and local cues on the rate of synchronization have not been fully studied. It is widespread that synchronization is achieved in the simultaneous presence of both global and local cues, such as intercellular coupling signals and external entrainment signals in terms of biological oscillators, and inter-neighbor coupling signals between follower nodes and central guiding signals in terms of groups of mobile autonomous agents. We prove in this paper that strength of the global cue is the only determinant of the rate of synchronization. More specifically, we prove that a stronger global cue means a faster rate of synchronization whereas a stronger local cue does not necessarily make the synchronization rate faster. Our results not only apply to the noise free case, but also apply to the case that the oscillator natural frequencies are subject to white noise. The analysis does not require the interplay to be symmetric or balanced. Simulation results are given to illustrate the proposed results.
在科学和工程领域，全局和局部线索作用下连接振荡器网络的同步现象无处不在。在过去几十年里，人们对化学、物理、力学尤其是生物学中连接振荡器的同步条件进行了大量研究。然而，全局和局部线索对同步速率的影响尚未得到充分研究。在全局和局部线索同时存在的情况下实现同步是很常见的，例如在生物振荡器方面，细胞间耦合信号和外部夹带信号；在移动自主代理群体方面，跟随节点之间的邻域耦合信号和中心引导信号。我们在本文中证明，全局线索的强度是同步速率的唯一决定因素。更具体地说，我们证明更强的全局线索意味着更快的同步速率，而更强的局部线索不一定会使同步速率更快。我们的结果不仅适用于无噪声情况，也适用于振荡器固有频率受白噪声影响的情况。该分析不要求相互作用是对称或平衡的。给出了仿真结果以说明所提出的结果。
