Globally Asymptotic Almost Automorphic Synchronization of Clifford-Valued RNNs With Delays

Abstract

In this paper, we consider a class of Clifford-valued recurrent neural networks (RNNs) with discrete and infinitely distributed delays. In order to overcome the non-commutativity of the multiplication of Clifford numbers, we first transform the Clifford-valued RNNs with discrete and infinitely distributed delays into real-valued systems based on the multiplication rule and properties of Clifford numbers. Then, we establish the existence and uniqueness of almost automorphic solutions for the neural networks under consideration by applying the contraction mapping principle, and we obtain the globally asymptotic almost automorphic synchronization of the neural networks under consideration by designing a novel state feedback controller and constructing an appropriate Lyapunov function. Finally, we present a numerical example to illustrate the feasibility of the results of this paper.

Keywords

• Clifford-valued recurrent neural networks
• time delay
• almost automorphic solution
• globally asymptotic synchronization