Pseudo-almost-periodic solutions of quaternion-valued RNNs with mixed delays via a direct method

Abstract

In this paper, we are concerned with the existence and global exponential stability of pseudo-almost-periodic solutions for quaternion-valued recurrent neural networks (RNNs) with time-varying delays. By using the Banach fixed point theorem and proof by contradiction, we directly study the existence and exponential stability of pseudo-almost-periodic solutions of the quaternion-valued systems under consideration without decomposing them into into real-or complex-valued systems. Our results obtained in this paper are new. Finally, we give a numerical example and computer simulation to illustrate the feasibility of our results.

Square-Mean Pseudo Almost Periodic Solutions for Quaternion-Valued Stochastic Neural Networks with Time-Varying Delays

“…Because all of these applications rely heavily on their dynamics, the study of various dynamical behaviors for quaternion-valued neural networks has received much attention of many scholars, and some results have been obtained for the stability [14][15][16], dissipativity [17], and pseudo almost periodicity [18,19] of quaternion-valued neural networks. In recent years, authors of [20,21] considered the existence and global exponential stability of pseudo almost periodic solutions and pseudo almost automorphic solutions for quaternion-valued neural networks by direct method. It should be noted that most studies on quaternion-valued neural network dynamic behaviors are concerned with the quaternion-valued deterministic neural networks, and so far, only a few results consider the stochastic quaternion-valued neural networks via a decomposing method [22,23].…”