For the convenience of computer simulation, the discrete-time systems in practice are often considered. In this paper, Discrete-time cellular neural networks (DTCNNs) are formulated and studied in a regime where they act as a switchboard for oscillating inputs. Several sufficient conditions are obtained to ensure DTCNNs with delays have a periodic orbit and this periodic orbit is globally attractive using a method based on the inequality method and the contraction mapping principle. Finally, simulations results are also discussed via one illustrative example.
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