Time-controllable combinatorial inner synchronization and outer synchronization of anti-star networks and its application in secure communication

In this paper, a time-controllable combinatorial inner synchronization and outer synchronization of anti-star networks, each of which consists of four-wing hyper-chaotic system as node dynamics, is investigated. Based on the adaptive technique and the stability of Lyapunov function, some sufficient conditions, which can ensure the realization of not only combinatorial inner synchronization within an anti-star network with unknown parameters and external perturbations in the computable time, but also combinatorial outer synchronization between different sub-networks with external perturbations in the computable time, are obtained. Moreover, a simple secure communication scheme, which is based on the adaptive combinatorial outer synchronization between different sub-networks under the influence of stochastic noise and time-delay, is presented. Numerical simulation results show the feasibility and validity of the proposed method.