Synchronization Mechanism for Controlled Complex Networks under Auxiliary Effect of Dynamic Edges

Abstract

The scope of complex dynamical networks (CDNs) with dynamic edges is very wide, as it is composed of a class of realistic networks including web-winding systems, communication networks, neural networks, etc. However, a classic research topic in CDNs, the synchronization control problem, has not been effectively solved for CDNs with dynamic edges. This paper will investigate the emergence mechanism of synchronization from the perspective of large-scale systems. Firstly, a CDN with dynamic edges is conceptualized as an interconnected coupled system composed of an edge subsystem (ES) and a node subsystem (NS). Then, based on the proposed improved directed matrix ES model and expanded matrix inequality, this paper overcomes the limitations of coupling term design in node models and the strong correlation of tracking targets between nodes and edges. Due to the effect of the synthesized node controller and the auxiliary effect of the ES, state synchronization can be realized in the CDN. Finally, through simulation examples, the validity and advantages of our work compared to existing methods are demonstrated.