Department of Mathematics, Bar-Ilan University, Ramat-Gan 5290002, Israel.
Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India.
Chaos. 2022 Apr;32(4):042101. doi: 10.1063/5.0087291.
Complex network theory has offered a powerful platform for the study of several natural dynamic scenarios, based on the synergy between the interaction topology and the dynamics of its constituents. With research in network theory being developed so fast, it has become extremely necessary to move from simple network topologies to more sophisticated and realistic descriptions of the connectivity patterns. In this context, there is a significant amount of recent works that have emerged with enormous evidence establishing the time-varying nature of the connections among the constituents in a large number of physical, biological, and social systems. The recent review article by Ghosh et al. [Phys. Rep. 949, 1-63 (2022)] demonstrates the significance of the analysis of collective dynamics arising in temporal networks. Specifically, the authors put forward a detailed excerpt of results on the origin and stability of synchronization in time-varying networked systems. However, among the complex collective dynamical behaviors, the study of the phenomenon of oscillation suppression and that of other diverse aspects of synchronization are also considered to be central to our perception of the dynamical processes over networks. Through this review, we discuss the principal findings from the research studies dedicated to the exploration of the two collective states, namely, oscillation suppression and chimera on top of time-varying networks of both static and mobile nodes. We delineate how temporality in interactions can suppress oscillation and induce chimeric patterns in networked dynamical systems, from effective analytical approaches to computational aspects, which is described while addressing these two phenomena. We further sketch promising directions for future research on these emerging collective behaviors in time-varying networks.
复杂网络理论为研究几个自然动态场景提供了一个强大的平台，其基础是相互作用拓扑结构与组成部分动态之间的协同作用。随着网络理论研究的快速发展，从简单的网络拓扑结构向更复杂和现实的连接模式描述转变已经变得非常必要。在这种情况下，有大量最近的研究工作涌现出来，大量证据表明，在大量物理、生物和社会系统中，组成部分之间的连接具有时变性质。Ghosh 等人最近的评论文章[Phys. Rep. 949, 1-63 (2022)]展示了分析时间网络中出现的集体动力学的重要性。具体来说，作者提出了关于时变网络系统中同步起源和稳定性的详细结果摘录。然而，在复杂的集体动力学行为中，对抑制振荡现象的研究以及对同步的其他不同方面的研究也被认为是我们对网络上动力学过程的认识的核心。通过这篇综述，我们讨论了专门探索两种集体状态（即时变网络中静态和移动节点的抑制振荡和嵌同）的研究工作的主要发现。我们描述了在网络动力学系统中，交互的暂时性如何抑制振荡并诱导嵌同模式，从有效的分析方法到计算方面，在解决这两个现象时都进行了描述。我们进一步勾勒了在时变网络中研究这些新兴集体行为的未来研究的有前途的方向。
