Saratov State University, 83, Astrakhanskaya, 410012, Saratov, Russia.
Yuri Gagarin State Technical University of Saratov, 77, Politehnicheskaya, Saratov, 410054, Russia and Saratov State University, 83, Astrakhanskaya, 410012, Saratov, Russia.
Phys Rev E. 2017 Dec;96(6-1):062312. doi: 10.1103/PhysRevE.96.062312. Epub 2017 Dec 18.
We report that explosive synchronization of networked oscillators (a process through which the transition to coherence occurs without intermediate stages but is rather characterized by a sudden and abrupt jump from the network's asynchronous to synchronous motion) is related to self-similarity of synchronous clusters of different size. Self-similarity is revealed by destructing the network synchronous state during the backward transition and observed with the decrease of the coupling strength between the nodes of the network. As illustrative examples, networks of Kuramoto oscillators with different topologies of links have been considered. For each one of such topologies, the destruction of the synchronous state goes step by step with self-similar configurations of interacting oscillators. At the critical point, the invariance of the phase distribution in the synchronized cluster with respect to the cluster size is reported.
我们报告称，网络振荡器的爆炸同步（一种无需中间阶段即可发生相干转变的过程，而是以网络从异步到同步运动的突然和突然跳跃为特征）与不同大小的同步簇的自相似性有关。通过在反向转变过程中破坏网络同步状态并随着网络节点之间的耦合强度的降低来观察到自相似性。作为说明性示例，已经考虑了具有不同链接拓扑的 Kuramoto 振荡器网络。对于每一种拓扑结构，同步状态的破坏都伴随着相互作用振荡器的自相似配置逐步进行。在临界点，报告了同步簇中相对于簇大小的相位分布的不变性。
