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This paper investigates the synchronization of reaction-diffusion neural networks (RDNNs) with distributed delay via quantized boundary control. To reduce the communication burden, a novel control strategy combined boundary control and logarithmic quantizer is proposed, and two controllers respectively subject to constant and adaptive coefficients are carried out. Worth mentioning that the adaptive feedback gain is a matrix in this paper rather than a one-dimensional variable in most of the existing literatures. Using the Lyapunov functional, the sufficient conditions for delay-dependent synchronization are obtained through linear matrix inequalities. The effectiveness of the proposed control strategy is illustrated via two examples.

This paper studies the intra/inter-layer synchronization and quasi-synchronization in two-layer coupled networks via event-triggered control, in which different layers have mutually independent topologies. First, based on Lyapunov stability theory and event-triggered thoughts, hybrid controllers are designed, respectively, for intra-layer synchronization (ALS) and inter-layer synchronization (RLS). Second, a novel event-triggered rule is proposed, under which intra-layer quasi-synchronization (ALQS) and inter-layer quasi-synchronization (RLQS) can be respectively realized, and the event-triggered frequency can be greatly reduced. Moreover, the upper bound of the synchronization error can be flexibly adjusted by changing the parameters in event-triggered conditions, and the Zeno phenomenon about event-triggered control is also discussed in this paper. Finally, numerical examples are provided to confirm the correctness and validity of the proposed scheme.

This paper regards the outer synchronization of multi-layer dynamical networks with additive couplings via aperiodically intermittent pinning control, in which different layers of each multi-layer network have different topological structures. First, a state-feedback intermittent pinning controller is designed in the drive and response configuration, and sufficient conditions to achieve the outer synchronization are derived based on the Lyapunov stability theory and matrix inequalities. Second, outer synchronization problem of multi-layer networks is discussed by setting an adaptive intermittent pinning controller; an appropriate Lyapunov function is selected to prove the criteria of synchronization between the drive multi-layer network and the response multi-layer network. Finally, three simulation examples are given to show the effectiveness of our control schemes.