Parameter and topology identification of delayed hypernetworks with stochastic perturbation

In the past two decades, large interconnected systems have been modeled as single-layer networks. In fact, various networks may interact and influence with each other to form the hypernetworks. As one of the most important problems in network science, topology identification of complex network has been widely studied in single-layer networks. On the contrary, topology identification of hypernetwork has received little attention. For a hypernetwork, different layers may have different delay, and noise is usually unavoidable. Therefore, the delayed hypernetwork with stochastic perturbation is put forward in this manuscript. By using synchronization-based identification method, the schemes to identify the unknown topology and system parameters are proposed. It is found that the unknown topology and system parameters of the drive network can be correctly identified, regardless of whether the topology of the response network is the same as that of the drive network. Numerical examples are illustrated to verify the effectiveness of the proposed algorithm. In addition, it is found that the identification time increases with the varying interval of coupling strengths, and the interval of the time delays and stochastic perturbations have opposite effects on the identification time.