Quaternion-valued Cellular Neural Networks Research Articles

Stability Analysis and Almost Periodic Solutions for Quaternion-Valued Cellular Neural Networks with Leakage Term on Time Scales

Stability Analysis and Almost Periodic Solutions for Quaternion-Valued Cellular Neural Networks with Leakage Term on Time Scales

Existence and global exponential stability of anti-periodic solutions for quaternion-valued cellular neural networks with time-varying delays

In this paper, we are concerned with a class of quaternion-valued cellular neural networks with time-varying transmission delays and leakage delays. By applying a continuation theorem of coincidence degree theory and the Wirtinger inequality as well as constructing a suitable Lyapunov functional, sufficient conditions are derived to ensure the existence and global exponential stability of anti-periodic solutions via direct approaches. Our results are completely new. Finally, numerical examples are also provided to show the effectiveness of our results.

On Pseudo Almost Automorphic Solutions to Quaternion-Valued Cellular Neural Networks With Delays

This manuscript considers quaternion-valued cellular neural networks with delays. Applying pseudo almost automorphic solution theory of delayed differential equations and pertinent inequalities, a new sufficient criterion to guarantee the existence and global exponentially stability of pseudo almost automorphic solutions of quaternion-valued cellular neural networks with delays are presented. Different from Xiang and Li, no assumption for kernel functions is necessary. Simulation results is displayed to verify the validity of theoretical analyses. Up to now, few scholars have dealt with this aspect. The obtained results of this manuscript are completely new and complement some previous studies to a certain extent.

Weighted pseudo-almost periodic solutions and global exponential synchronization for delayed QVCNNs

In this paper, we study the existence of weighted pseudo-almost periodic solutions and the global exponential synchronization of delayed quaternion-valued cellular neural networks (QVCNNs). Firstly, we use the Banach fixed point theorem to establish the existence of weighted pseudo-almost periodic solutions for this class of QVCNNs. Then, under the condition that the drive system has a unique weighted pseudo-almost periodic solution, by designing a state-feedback controller and constructing suitable Lyapunov functions, we see that the drive–response structure of delayed QVCNNs with weighted pseudo-almost periodic coefficients achieve global exponential synchronization. Finally, a numerical example is given to illustrate the feasibility of our results.

Pseudo almost automorphic solutions of quaternion-valued neural networks with infinitely distributed delays via a non-decomposing method

In this paper, we consider the existence and global exponential stability of pseudo almost automorphic solutions to quaternion-valued cellular neural networks with infinitely distributed delays. Unlike most previous studies of quaternion-valued cellular neural networks, we do not decompose the systems under consideration into real-valued or complex-valued systems, but rather directly study quaternion-valued systems. Our method and the results of this paper are new. An example is given to show the feasibility of our main results.

Pseudo almost periodic solutions for quaternion-valued cellular neural networks with discrete and distributed delays

This paper is concerned with a class of quaternion-valued cellular neural networks with discrete and distributed delays. By using the exponential dichotomy of linear systems and a fixed point theorem, sufficient conditions are derived for the existence and global exponential stability of pseudo almost periodic solutions of this class of neural networks. Finally, a numerical example is given to illustrate the feasibility of the obtained results.

The global exponential pseudo almost periodic synchronization of quaternion-valued cellular neural networks with time-varying delays

Abstract In this paper, we consider the problem of the pseudo almost periodic synchronization of quaternion-valued cellular neural networks (QVCNNs) with time-varying delays. Firstly, we use the Banach fixed point theorem to obtain the existence of pseudo almost periodic solutions of QVCNNs with time varying delays. Then, by designing a novel and very general nonlinear state-feedback controller, and constructing suitable Lyapunov functions, we obtain that the drive-response structure of QVCNNs with pseudo almost periodic coefficients can realize the global exponential synchronization. Our results are completely new. Finally, a numerical example is given to illustrate the feasibility of our results.

Existence and global exponential stability of periodic solutions for quaternion-valued cellular neural networks with time-varying delays

Abstract In this paper, a class of quaternion-valued cellular neural networks (QVCNNs) with time-varying delays is considered. By using the continuation theorem of Mawhin’s coincidence degree theory, the existence of periodic solutions for QVCNNs is obtained. By constructing a suitable Lyapunov function, some sufficient conditions are derived to guarantee the global exponential stability of periodic solutions for QVCNNs. Finally, two examples are given to illustrate the effectiveness of the obtained results.