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In this paper, a class of neural networks with time-varying delays are investigated for the first time using a periodically intermittent control technique. First, some new and useful stabilization criteria and synchronization conditions based on p-norm are derived by introducing multi-parameters and using the Lyapunov functional technique. For ∞-norm, using the analysis technique, some novel conditions ensuring exponential stability and synchronization are also obtained. It is worth noting that the methods used in this paper are totally different from the corresponding previous works and the obtained conditions are less conservative. Particularly, the traditional assumptions on control width and time delay are removed in this paper. Finally, some numerical simulations are given to verify the theoretical results.