Function projective synchronization in complex networks with switching topology and stochastic effects

Although function projective synchronization in complex dynamical networks has come into the limelight in recent years, litter research has been published on the problem in the dynamical networks with switching topology and stochastic effects. This study aims to fill the gap. In this paper, the problem of function projective synchronization is investigated for complex networks with switching topology and stochastic effects. A hybrid feedback control method is designed to achieve function projective synchronization for the complex network. Using the property of martingale and Gronwally’ inequality, we obtain some conditions to guarantee that the complex network can realize mean square synchronization and mean square exponential synchronization, respectively. Furthermore, we also present a probability approach to the method of Lyapunov functionals to analyze function projective synchronization in the dynamical network under a particular assumption. Our approaches not only can replace the LaSalle-type theorem but also allow improvements of existing results in the literature. In particular, the study also presents an equivalent way of regarding Itô’ integral, which may be a useful tool to deal with the problem of synchronization in variety of complex dynamical networks with stochastic effects. Finally, some numerical examples are provided to demonstrate the effectiveness of the proposed approach.