Almost Periodic Synchronization for Quaternion‐Valued Neural Networks with Time‐Varying Delays

Abstract

This paper focuses on the global exponential almost periodic synchronization of quaternion-valued neural networks with timevarying delays. By virtue of the exponential dichotomy of linear differential equations, Banach's fixed point theorem, Lyapunov functional method, and differential inequality technique, some sufficient conditions are established for assuring the existence and global exponential synchronization of almost periodic solutions of the delayed quaternion-valued neural networks, which are completely new. Finally, we give one example with simulation to show the applicability and effectiveness of our main results.

Global Asymptotic Almost Periodic Synchronization of Clifford‐Valued CNNs with Discrete Delays

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Existence and global exponential stability of almost periodic solution for quaternion‐valued high‐order Hopfield neural networks with delays via a direct method

“…On the other hand, since quaternion‐valued neural networks are superior to real‐valued and complex‐valued neural networks in processing high‐dimensional data and spatial transforms, in recent years, the study of quaternion‐valued neural networks has become a hot issue . However, due to the noncommutativity of the quaternion multiplication, the main method for studying the dynamical behavior of quaternion‐valued neural network systems is to decompose the considered neural network systems into real‐valued or complex‐valued systems …”

New Results on Exponential Stability of Competitive Neural Networks with Multi‐Proportional Delays

“…Since, in reality, time delays cannot be avoided and it is well known that the dynamics of neural networks plays a crucial role in their implementation and applications, recently, many researchers have paid much attention to the dynamics analysis of neural networks with various types of delays [6][7][8][9][10][11][12][13][14][15][16][17][18][19]. For example, the authors of [17][18][19][20][21][22][23][24] studied the global stability for CNNs; the authors of [23] investigated the multistability for CNNs; the authors of [24] investigated multistability and multiperiodicity of CNNs; the authors of [25] studied the existence and global exponential stability of anti-periodic solutions for CNNs; and the authors of [26][27][28] However, there are very few existing works dealing with the dynamics of CNNs with the proportional delay.…”