Stabilization of Nonautonomous Recurrent Neural Networks With Bounded and Unbounded Delays on Time Scales.
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A class of nonautonomous recurrent neural networks (NRNNs) with time-varying delays is considered on time scales. Bounded delays and unbounded delays have been taken into consideration, respectively. First, a new generalized Halanay inequality on time scales is constructed by time-scale theory and some analytical techniques. Based on this inequality, the stabilization of NRNNs with bounded delays is discussed on time scales. The results are also applied to the synchronization of a class of drive-response NRNNs. Furthermore, the stabilization of NRNNs with unbounded delays is investigated. Especially, the stabilization of NRNNs with proportional delays is obtained without any variable transformation. The obtained generalized Halanay inequality on time scales develops and extends some existing ones in the literature. The stabilization criteria for the NRNNs with bounded or unbounded delays cover the results of continuous-time and discrete-time NRNNs and hold the results for the systems that involved on time interval as well. Some examples are given to demonstrate the validity of the results. An application to image encryption and decryption is addressed.