Almost Automorphic Solutions for Quaternion-Valued Hopfield Neural Networks with Mixed Time-Varying Delays and Leakage Delays

Abstract

This paper considers a class of quaternion-valued Hopfield neural networks with mixed time-varying delays and leakage delays. By utilizing the exponential dichotomy of linear differential equations, Banach’s fixed point theorem and differential inequality techniques, the authors obtain some sufficient conditions to ensure the existence and global exponential stability of almost automorphic solutions for this class of quaternion-valued neural networks. The results are completely new. Finally, the authors give an example to illustrate the feasibility of the results.