The synchronized dynamics of time-varying networks

TL;DR

This paper reviews the emergence of synchronization in time-varying networks, focusing on two main frameworks: adaptive or externally influenced link changes, and movement-driven structural evolution, highlighting recent advances and open challenges.

Contribution

It provides a comprehensive overview of key results in synchronization within time-varying networks, emphasizing two paradigmatic models and discussing future research directions.

Findings

Synchronization can emerge in networks with dynamic topologies.

Two main frameworks: link adaptation and node movement.

Open problems include modeling complexity and real-world applications.

Abstract

Over the past two decades, complex network theory provided the ideal framework for investigating the intimate relationships between the topological properties characterizing the wiring of connections among a system's unitary components and its emergent synchronized functioning. An increased number of setups from the real world found therefore a representation in term of graphs, while more and more sophisticated methods were developed with the aim of furnishing a realistic description of the connectivity patterns under study. In particular, a significant number of systems in physics, biology and social science features a time-varying nature of the interactions among their units. We here give a comprehensive review of the major results obtained by contemporary studies on the emergence of synchronization in time-varying networks. In particular, two paradigmatic frameworks will be described in details. The first encompasses those systems where the time dependence of the nodes' connections is due to adaptation, external forces, or any other process affecting each of the links of the network. The second framework, instead, corresponds to the case in which the structural evolution of the graph is due to the movement of the nodes, or agents, in physical spaces and to the fact that interactions may be ruled by space-dependent laws in a way that connections are continuously switched on and off in the course of the time. Finally, our report ends with a short discussion on promising directions and open problems for future studies.