Discrete analogue of impulsive recurrent neural networks with both discrete and finite distributive asynchronous time-varying delays.

Abstract

This paper studies the dynamical characteristics of discrete analogue of impulsive recurrent neural networks with both discrete and finite distributed asynchronous time-varying delays. Firstly, the discrete impulsive system of the corresponding continuous-time model is reformed by impulsive maps and semi-discrete method. Secondly, by employing a famous delay impulsive differential inequality, several novel sufficient conditions are derived to ensure the uniqueness of equilibrium point and its global exponential stability in Lagrange sense for the discussed discrete-time impulsive system. Meanwhile, it is illustrated that the discrete-time analogue retains the uniqueness of equilibrium point of the corresponding continuous-time model, and some corollaries follow. Finally, one example is given to demonstrate the validity of our obtained results.