Gao Jian, Efstathiou Konstantinos
Bernoulli Institute for Mathematics, Computer Science, and Artificial Intelligence, University of Groningen, P.O. Box 407, 9700 AK, Groningen, The Netherlands.
Division of Natural and Applied Sciences and Zu Chongzhi Center for Mathematics and Computational Science, Duke Kunshan University, No. 8 Duke Avenue, Kunshan 215316, China.
Phys Rev E. 2020 Feb;101(2-1):022302. doi: 10.1103/PhysRevE.101.022302.
We consider the synchronization of oscillators in complex networks where there is an interplay between the oscillator dynamics and the network topology. Through a remarkable transformation in parameter space and the introduction of virtual frequencies we show that Kuramoto oscillators on annealed networks, with or without frequency-degree correlation, and Kuramoto oscillators on complete graphs with frequency-weighted coupling can be transformed to Kuramoto oscillators on complete graphs with a rearranged, virtual frequency distribution and uniform coupling. The virtual frequency distribution encodes both the natural frequency distribution (dynamics) and the degree distribution (topology). We apply this transformation to give direct explanations to a variety of phenomena that have been observed in complex networks, such as explosive synchronization and vanishing synchronization onset.
我们考虑复杂网络中振子的同步问题，其中振子动力学与网络拓扑之间存在相互作用。通过参数空间中的显著变换以及虚拟频率的引入，我们表明，退火网络上具有或不具有频率-度相关性的Kuramoto振子，以及具有频率加权耦合的完全图上的Kuramoto振子，可以变换为具有重新排列的虚拟频率分布和均匀耦合的完全图上的Kuramoto振子。虚拟频率分布编码了自然频率分布（动力学）和度分布（拓扑）。我们应用这种变换对复杂网络中观察到的各种现象给出直接解释，例如爆发性同步和同步起始消失。
