Research and Educational Center "Artificial Intelligence Systems and Neurotechnology," Yuri Gagarin State Technical University of Saratov, Saratov 410054, Russia.
Potsdam Institute for Climate Impact Research, 14473 Potsdam, Germany.
Phys Rev E. 2018 Aug;98(2-1):022320. doi: 10.1103/PhysRevE.98.022320.
In this paper we study the dynamics of a multiplex multilayer network, where each layer is composed of identical Kuramoto-Sakaguchi phase oscillators with nonlocal coupling. We focus on a three-layer multiplex network and observe a specific form of multiplex network behavior, the macroscopic chimeralike state. It is decomposed by a splitting of the layers with initially close dynamics into subgroups. The first group consists of two layers performing one type of dynamics, whereas the rest perform the other type, after the introduction of interlayer coupling. Based on an intensive computational analysis, we show that areas of macroscopic chimeralike states are observed close to the critical transition points of intralayer (microscopic) states in the parameter space. We find that this macroscopic chimeralike state is excited at weak and medium interlayer coupling strength, wherein the interlayer phase lag here plays an important role, since this is a network parameter which controls macroscopic dynamics and transforms boundaries between intralayer states. The obtained numerical results are validated analytically by considering the multiplex network dynamics using the Ott-Antonsen reduction of the governing network equations.
在本文中，我们研究了一个复合同步多层网络的动力学，其中每个层都由具有非局部耦合的相同 Kuramoto-Sakaguchi 相振荡器组成。我们专注于一个三层复合同步网络，并观察到一种特定形式的复合同步网络行为，即宏观嵌同状态。它通过将最初具有相似动力学的层进行分组来分解。第一个组由两个层执行一种类型的动力学组成，而其余层在引入层间耦合后执行另一种类型的动力学。通过深入的计算分析，我们表明在参数空间中接近层内（微观）状态的临界跃迁点的区域观察到宏观嵌同状态。我们发现，这种宏观嵌同状态在弱和中等层间耦合强度下被激发，其中层间相位滞后在这里起着重要作用，因为这是一个控制宏观动力学并改变层内状态之间边界的网络参数。通过使用 Ott-Antonsen 对控制网络方程的约化来考虑复合同步网络动力学，我们从理论上验证了所得到的数值结果。
