Louzada V H P, Araújo N A M, Andrade J S, Herrmann H J
Computational Physics, IfB, ETH-Honggerberg, Wolfgang-Pauli-Strasse 27, 8093 Zurich, Switzerland.
Sci Rep. 2013 Nov 21;3:3289. doi: 10.1038/srep03289.
Global synchronization in a complex network of oscillators emerges from the interplay between its topology and the dynamics of the pairwise interactions among its numerous components. When oscillators are spatially separated, however, a time delay appears in the interaction which might obstruct synchronization. Here we study the synchronization properties of interconnected networks of oscillators with a time delay between networks and analyze the dynamics as a function of the couplings and communication lag. We discover a new breathing synchronization regime, where two groups appear in each network synchronized at different frequencies. Each group has a counterpart in the opposite network, one group is in phase and the other in anti-phase with their counterpart. For strong couplings, instead, networks are internally synchronized but a phase shift between them might occur. The implications of our findings on several socio-technical and biological systems are discussed.
复杂振荡器网络中的全局同步源于其拓扑结构与众多组件之间成对相互作用的动力学之间的相互作用。然而，当振荡器在空间上分离时，相互作用中会出现时间延迟，这可能会阻碍同步。在这里，我们研究了网络之间存在时间延迟的互连振荡器网络的同步特性，并分析了作为耦合和通信延迟函数的动力学。我们发现了一种新的呼吸同步状态，其中每个网络中出现两组以不同频率同步的振荡器。每组在相反的网络中有一个对应组，一组与其对应组同相，另一组与其对应组反相。相反，对于强耦合，网络内部是同步的，但它们之间可能会出现相位偏移。我们讨论了我们的发现对几个社会技术和生物系统的影响。
