Quasi-Synchronization of Neural Networks with Diffusion Effects via Intermittent Control of Regional Division

Abstract In this paper, we investigate the quasi-synchronization issue of an array of Diffusion Effects Neural Networks (DENNs) with time-varying coupling strength. Two kinds of quasi-synchronization scenarios are discussed. One is self-synchronization and the other is tracking-synchronization. In order to lower the communication loads and reduce the control resource consumption, we propose a new control scheme called intermittent control of reginal division to make the synchronization error within a bounded scope. In this novel control scheme, the non-negative real region is divided into three subregions in advance and an auxiliary Lyapunov function is imported to decide the work time and the rest time by its relationship with three subregions. Moreover, by using rigorous mathematic analysis, we obtain sufficient conditions for the two kinds of quasi-synchronization modes of DENNs under the as-proposed control scheme. Nonidentical term in the network is viewed as external disturbance about to be compensated by the controller. The result shows that the upper bound of synchronization error will be progressively regulated by the parameters in chosen divided region. Several numerical examples are also presented to verify the validity of our theory.