Yufeng Zhou

The quasisynchronization of nonidentically coupled dynamical networks (NCDNs) with proportional delay is achieved by the event-triggered mechanism (ETM). Heterogeneity and proportional delay greatly increase the difficulty on synchronization of NCDNs. As an unbounded delay in the coupling term, proportional delay is dealt with by the comparison principle, constructing parameter equations, and contradiction method. Moreover, different impulsive effects based on ETM are taken into account to reduce the burden of communication, and the quasisynchronization criteria for NCDNs are derived by the impulsive comparison principle and extended variable parameter formula. The synchronization errors and the exponential convergence rates under different impulsive effects are obtained. It is proven that the proposed ETM can avoid Zeno behavior. Finally, examples show the effectiveness of the proposed control scheme.

Master-slave synchronization of two delayed neural networks with adaptive controller has been studied in recent years; however, the existing delays in network models are bounded or unbounded with some derivative constraints. For more general delay without these restrictions, how to design proper adaptive controller and prove rigorously the convergence of error system is still a challenging problem. This article gives a positive answer for this problem. By means of the stability result of unbounded delayed system and some analytical techniques, we prove that the traditional centralized adaptive algorithms can achieve global asymptotical synchronization even if the network delays are unbounded without any derivative constraints. To describe the convergence speed of the synchronization error, adaptive designs depending on a flexible ω-type function are also provided to control the synchronization error, which can lead exponential synchronization, polynomial synchronization, and logarithmically synchronization. Numerical examples on delayed neural networks and chaotic Ikeda-like oscillator are presented to verify the adaptive designs, and we find that in the case of unbounded delay, the intervention of ω-type function can promote the realization of synchronization but may destroy the convergence of control gain, and this however will not happen in the case of bounded delay.

This article considers the quasisynchronization of memristive neural networks (MNNs) with communication delays via event-triggered impulsive control (ETIC). In view of the limited communication and bandwidth, we adopt a novel switching event-triggered mechanism (ETM) that not only decreases the times of controller update and the amount of data sent out but also eliminates the Zeno behavior. By using an appropriate Lyapunov function, several algebraic conditions are given for quasisynchronization of MNNs with communication delays. More important, there is no restriction on the derivation of the Lyapunov function, even if it is an increasing function over a period of time. Then, we further propose a switching ETM depending on communication delays and aperiodic sampling, which is more economical and practical and can directly avoid Zeno behavior. Finally, two simulations are presented to validate the effectiveness of the proposed results.