Stepanov-like Asymptotical Almost Periodic Solutions Of Quaternion-valued Hopfield Neural Networks

This paper relies on the concept of Stepanov-like asymptotical almost periodic func-tions,which is more generalized than the concept of Stepanov almost periodic functions.Based on the given concepts and lemmas,this article discusses the Stepanov-like asymp-totical almost periodic solutions of a class of specific neural network models.In the main part,the article presents and validates several essential and important properties related to Stepanov-like asymptotical almost periodic functions.Based on these basic conclusion-s,the premise conditions of the existence uniqueness and globally exponential stability of Stepanov-like asymptotical almost periodic solutions of quaternion-valued Hopfield neural networks with time-varying delays and distributed delays are obtained by applying the contraction mapping principle.Finally,a concrete numerical example is adopted to test.the validity and rationality of the important conclusions obtained in this paper.