Existence And Global Exponential Stability Of Pseudo Almost Periodic Solutions For Two Kinds Of Quaternion-valued Neural Networks

In this paper,we study the existence and global exponential stability of pseudo almost periodic solutions for two kinds of quaternion-valued neural networks(QVNNs).Unlike most previous QVNNs,the connection weights of the considered QVNNs are quaternions.First of all,we study a kind of quaternion-valued cellular neural networks(QVCNNs)with time-varying delays and distributed delays.We study the existence of pseudo almost periodic solutions for QVCNNs by using a nondecomposing method and applying the contraction fixed point theorem and differential inequality techniques,and we research the global exponential stability of pseudo almost periodic solutions for QVCNNs by using the proof of contradiction;secondly,we study another kind of quaternion-valued high-order Hopfield neural networks(QVHHNNs)with leakage delays.By using similar methods above,we study the existence and global exponential stability of pseudo almost periodic solutions for this kind of QVHHNNs;finally,examples are given to illustrate the validity and feasibility of our main conclusions.The methods of this paper can be used to study the existence and stability of other types of solutions of other types of QVNNs.