Synchronization of an evolving complex hyper-network

An evolving hyper-network model is proposed for better describing some complex systems. A concept of joint degree is introduced, and the evolving mechanism of the hyper-network is given with respect to the joint degree. The hyper-degree distribution of this evolving hyper-network is derived based on a rate equation method and is shown to obey a power law, non-Gaussian distribution. Furthermore, the synchronization in a hyper-network of coupled dynamical systems is investigated for the first time. By calculating the joint degree matrix, several simple yet useful synchronization criteria are obtained and are illustrated numerically in specific examples.