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This paper presents new theoretical results on the invariance and attractivity of memristor-based cellular neural networks (MCNNs) with time-varying delays. First, sufficient conditions to assure the boundedness and global attractivity of the networks are derived. Using state-space decomposition and some analytic techniques, it is shown that the number of equilibria located in the saturation regions of the piecewise-linear activation functions of an n-neuron MCNN with time-varying delays increases significantly from 2(n) to 2(2n2)+n) (2(2n2) times) compared with that without a memristor. In addition, sufficient conditions for the invariance and local or global attractivity of equilibria or attractive sets in any designated region are derived. Finally, two illustrative examples are given to elaborate the characteristics of the results in detail.

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In this paper, we investigate the global synchronization control problem for memristive neural networks (MNNs) with time-varying delay. A novel event-triggered controller is introduced with the linear diffusive term and discontinuous sign term. In order to greatly reduce the computation cost of the controller under certain event-triggering condition, two event-based control schemes are proposed with static event-triggering condition and dynamic event-triggering condition. Some sufficient conditions are derived by these control schemes to ensure the response MNN to be synchronized with the driving one. Furthermore, under certain event-triggering conditions, a positive lower bound is achieved for the interexecution time to guarantee that Zeno behavior cannot be executed. Finally, numerical simulations are provided to substantiate the effectiveness of the proposed theoretical results.

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