Stability analysis of quaternion-valued neural networks with both discrete and distributed delays

Tu, Zhengwen; Zhao, Yongxiang; Ding, Nan; Feng, Yuming; Zhang, Wei

doi:10.1016/j.amc.2018.09.049

Cited by 65 publications

(58 citation statements)

References 47 publications

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“…In practice, the main advantage of using quaternion is that it can view and operate three-dimensional or four-dimensional vectors as a single entity that significantly reduces computational complexity in multidimensional problems and by employing quaternion variables can achieve efficient information processing directly [23][24][25]. Therefore, QVNNs have been successfully implemented in body images, attitude control of satellites, computer graphics, 3D wind forecasting, 4D signals, color-face recognition, and vector sensor processing [26][27][28][29][30][31][32][33]. The problem of global µ stability for QVNNs with mixed time delays was studied in [22].…”

Section: Introductionmentioning

confidence: 99%

Global Mittag–Leffler Stability and Stabilization Analysis of Fractional-Order Quaternion-Valued Memristive Neural Networks

et al. 2020

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This paper studies the global Mittag–Leffler stability and stabilization analysis of fractional-order quaternion-valued memristive neural networks (FOQVMNNs). The state feedback stabilizing control law is designed in order to stabilize the considered problem. Based on the non-commutativity of quaternion multiplication, the original fractional-order quaternion-valued systems is divided into four fractional-order real-valued systems. By using the method of Lyapunov fractional-order derivative, fractional-order differential inclusions, set-valued maps, several global Mittag–Leffler stability and stabilization conditions of considered FOQVMNNs are established. Two numerical examples are provided to illustrate the usefulness of our analytical results.

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Section: Introductionmentioning

confidence: 99%

Global Mittag–Leffler Stability and Stabilization Analysis of Fractional-Order Quaternion-Valued Memristive Neural Networks

et al. 2020

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“…Thereupon, it is necessary to consider QVNN. In recent years, a few results on dynamical properties of QVNN, including stability, periodicity, dissipativity, and passivity, have appeared [30][31][32][33]. Moreover, the memristor, as a fourth fundamental circuit element, was reported in Nature.…”

Section: Introductionmentioning

confidence: 99%

Fixed time synchronization of delayed quaternion-valued memristor-based neural networks

et al. 2020

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This paper investigates the fixed time synchronization issue for a class of quaternion-valued memristor-based neural networks (QVMNN) at the presence of time varying delays. Differential inclusion and fixed time stability theory are used, and new synchronization conditions are formulated to achieve the synchronization of delayed QVMNN within a fixed time based on a Lyapunov function and a suitable controller. The feasibility of the proposed method is shown through numerical simulations.

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“…Therefore, the research on quaternion-valued neural networks has become a hot topic in the theory and applications of neural networks. However, due to the noncommutativity of quaternion multiplication, the results of quaternion-valued neural network dynamics are very few [32][33][34][35][36][37][38][39][40][41]. Especially, the results obtained by a method of not decomposing quaternionvalued systems into real-or complex-valued systems are even rarer.…”

Section: Introductionmentioning

confidence: 99%

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

Xiang

2020

J Inequal Appl

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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.

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Stability analysis of quaternion-valued neural networks with both discrete and distributed delays

Cited by 65 publications

References 47 publications

Global Mittag–Leffler Stability and Stabilization Analysis of Fractional-Order Quaternion-Valued Memristive Neural Networks

Global Mittag–Leffler Stability and Stabilization Analysis of Fractional-Order Quaternion-Valued Memristive Neural Networks

Fixed time synchronization of delayed quaternion-valued memristor-based neural networks

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

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