Convergence of non-autonomous discrete-time Hopfield model with delays

This paper is concerned with boundedness, convergence of solution of a class of non-autonomous discrete-time delayed Hopfield neural network model. Using the inequality technique, we obtain some sufficient conditions ensuring the boundedness of solutions of the discrete-time delayed Hopfield models in time-varying situation. Then, by exploring intrinsic features between non-autonomous system and its asymptotic equations, several novel sufficient conditions are established to ensure that all solutions of the networks converge to the solution of its asymptotic equations. Especially, for case of asymptotic autonomous system or asymptotic periodic system, we obtain some sufficient conditions ensuring all solutions of original system convergent to equilibrium or periodic solution of asymptotic system, respectively. An example is provided for demonstrating the effectiveness of the global stability conditions presented. Our results are not only presented in terms of system parameters and can be easily verified but also are less restrictive than previously known criteria.