Enhancing Synchronizability of Diffusively Coupled Dynamical Networks: A Survey

In this paper, we review the literature on enhancing synchronizability of diffusively coupled dynamical networks with identical nodes. The last decade has witnessed intensive investigations on the collective behavior over complex networks and synchronization of dynamical systems is the most common form of collective behavior. For many applications, it is desired that the synchronizability-the ability of networks in synchronizing activity of their individual dynamical units-is enhanced. There are a number of methods for improving the synchronization properties of dynamical networks through structural perturbation. In this paper, we survey such methods including adding/removing nodes and/or edges, rewiring the links, and graph weighting. These methods often try to enhance the synchronizability through minimizing the eigenratio of the Laplacian matrix of the connection graph-a synchronizability measure based on the masterstability-function formalism. We also assess the performance of the methods by numerical simulations on a number of real-world networks as well as those generated through models such as preferential attachment, Watts-Strogatz, and Erdos-Renyi.