Synchronization and control of hyper-networks and colored networks

Abstract

In this chapter, hyper-networks and colored networks corresponding to hyper-graphs and colored graphs in mathematics are presented, which can be used to model real large-scale systems, such as neuronal networks, metabolic networks, social relationship networks, scientific collaboration networks, and so on. Firstly, similarly to the BA scale-free network, both growth and preferential attachment mechanisms are adopted to generate some evolving hyper-network models, including uniform and nonuniform hyper-networks. Secondly, a uniform dynamical hypernetwork model is built and its synchronization is investigated using joint-degree matrix. Thirdly, a colored network with same-dimensional node dynamics is presented. The synchronization and control of both edge-colored and colored networks are studied. Finally, a general colored network with different-dimensional node dynamics is presented and its generalized matrix projective synchronization is achieved by applying open-plus-closed-loop control.