Synchronization for dynamic complex networks combining degree distribution and eigenvector criteria

A complex network is composed of nodes and connecting edges, which can be applied to describe the structure of many real systems. Synchronization is an important behavior of dynamic complex networks. The traditional methods, such as changing network coupling mode and external control strategies, etc., cannot achieve complete network synchronization. In order to solve the network synchronization problem, in the paper, we propose a method of constructing an improved small-world network that combines degree distribution and eigenvector criteria from the viewpoint of the topology of complex networks and analyze the effects of network topology on synchronization capability. Aiming at the problem that synchronization capability is suppressed due to the uneven degree distribution during the construction of network model, we present a method of degree distribution connection to select the nodes with a smaller degree preferentially when reconnecting edges. Combining eigenvector Criteria, we also present a method of building Enhanced Synchronization Small-World, which deletes connecting edges by selecting the nodes with a larger degree and reconnects edges according to the eigenvector criterion. On this basis, we further analyze the impacts of differences in different network topologies on synchronization capability. The experimental results show that our solution is effective to construct network through the combination of degree distribution and eigenvector criterion, which can solve the network synchronization problem well by improving network topology.