Synchronization mechanisms in coupled neural networks with time-varying topologies: From edge-level rewiring to network-wide collective behaviors

This study investigates the synchronization issue for coupled neural networks with time-varying communication topologies, with a particular focus on establishing the cross-scale relationship between microscopic-scale edge rewiring dynamics and macroscopic network synchronization behaviors. Firstly, some characteristic parameters are introduced to quantify the dynamic rewiring behaviors of each edge within the network. Leveraging these parameters and employing the techniques such as Jensen's inequality and Barbalat's lemma, some synchronization conditions related to the dynamic rewiring characteristics of edges are established. Based on these conditions, the impact of edge rewiring dynamics on network synchronization is analyzed. Our analysis reveals that the synchronization becomes more likely when: (1) the time required for the switching network topologies to achieve joint connectivity is shorter, and (2) the duration each edge exists within a joint connectivity period is longer. Notably, the derived synchronization conditions impose no requirement for a positive lower bound on the communication topologies’ dwell time. In contrast to the classical average dwell-time approach, these conditions impose fewer constraints on topology switching frequency and exhibit wider applicability. Furthermore, these synchronization conditions impose weak connectivity requirements on the switching topologies, necessitating only joint connectivity. Finally, some numerical experiments confirm the validity of the theoretical results.