The Existence and Global Exponential Stability of $${\varvec{\mu }}$$-Pseudo Almost Periodic Solutions of Clifford-Valued Semi-linear Delay Differential Equations and an Application

Abstract

In this paper, we consider Clifford-valued semi-linear delay differential equations. Without decomposing the considered differential equations into real-valued equations, we first transform the Clifford-valued differential equations into their equivalent integral equations. Then, by using the Banach fixed point theorem and inequality techniques, we obtain sufficient conditions to ensure the existence and global exponential stability of $$\mu $$-pseudo almost periodic solutions for the Clifford-valued differential equations under consideration. Finally, as an application of our proposed method, we study the existence and global exponential stability of $$\mu $$-pseudo almost periodic solutions of Clifford-valued recurrent neural networks. Our methods and results are new.