Periodic solutions for nonautonomous discrete-time neural networks

In this paper, we theoretically prove the existence of periodic solutions for a nonautonomous discrete-time neural networks by using the topological degree theory. Sufficient conditions are also obtained for the existence of an asymptotically stable periodic solution. As a special case, we obtain the existence of a fixed point to the corresponding autonomous discrete-time neural networks which corrects the error in [W.R. Zhao, W. Lin, R.S. Liu, J. Ruan, Asymptotical stability in discrete-time neural networks, IEEE Trans. Circuits Syst. I 49 (2002) 1516–1520]. Numerical simulations are given at the end of the paper.