Existence and Stability of Pseudo Almost Periodic Solution for Neutral Type High-Order Hopfield Neural Networks with Delays in Leakage Terms on Time Scales

Abstract

Using the exponential dichotomy of linear dynamic equations on time scales, a fixed point theorem and the theory of calculus on time scales, we obtain some sufficient conditions for the existence and global exponential stability of pseudo almost periodic solutions for a class of neutral type high-order Hopfield neural networks with delays in leakage terms on time scales. Our results show that the continuous-time neural network and its discrete-time analogue have the same dynamical behaviors. Finally, we give a numerical example and simulation to illustrate the feasibility of our results. Results of this paper are completely new even if the time scale $$\mathbb {T}=\mathbb {R}$$T=R or $$\mathbb {Z}$$Z.