School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China.
State Key Laboratory of Advanced Electromagnetic Engineering and Technology, School of Electrical and Electronic Engineering, Huazhong University of Science and Technology, Wuhan 430074, China.
Phys Rev E. 2019 Jul;100(1-1):012209. doi: 10.1103/PhysRevE.100.012209.
A second-order continuous synchronization has been well documented for the classic Kuramoto model. Here we generalize the classic Kuramoto model by incorporating a low-pass filter (LPF) in the coupling, which serves as a simple form of indirect coupling through a common external dynamic environment. We uncover that a first-order explosive synchronization turns out to be a very generic phenomenon in this generalized Kuramoto model with LPF. We establish theoretical results by providing a rigorous analytical treatment, which is validated by conducting extensive numerical simulations. Our study provides a new root for the emergence of first-order explosive synchronization, which could substantially deepen the understanding of the underlying mechanism of a first-order phase transition towards synchronization in coupled dynamical networks.
二阶连续同步已被很好地记录在经典 Kuramoto 模型中。在这里，我们通过在耦合中加入一个低通滤波器（LPF）来推广经典 Kuramoto 模型，这是通过共同的外部动态环境进行间接耦合的一种简单形式。我们发现，在这个具有 LPF 的广义 Kuramoto 模型中，一阶爆炸同步是一种非常普遍的现象。我们通过严格的分析处理提供了理论结果，并通过广泛的数值模拟进行了验证。我们的研究为一阶爆炸同步的出现提供了一个新的根源，这可能会大大深化对耦合动力网络中一阶相变向同步的底层机制的理解。
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