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This paper deals with the synchronization for discrete-time coupled neural networks (DTCNNs), in which stochastic perturbations and multiple delays are simultaneously involved. The multiple delays mean that both discrete time-varying delays and distributed delays are included. Time-triggered impulsive control (TTIC) is proposed to investigate the synchronization issue of the DTCNNs based on the recently proposed impulsive control scheme for continuous neural networks with single time delays. Furthermore, a novel event-triggered impulsiv