Global μ-stability criteria for quaternion-valued neural networks with unbounded time-varying delays

Liu, Yang; Zhang, Dandan; Lu, Jianquan; Cao, Jinde

doi:10.1016/j.ins.2016.04.033

Cited by 168 publications

(47 citation statements)

References 39 publications

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“…In recent years, the quaternion-valued neural networks, as an extension of the real-valued neural networks and the complex-valued neural networks [6,7], research has become a hot topic. It should be pointed out that, at present, almost all the investigations on quaternion-valued neural networks are mainly dealing with the stability, robustness, or dissipation of the equilibrium of the neural networks; see [8][9][10][11][12][13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

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

Meng

2018

Complexity

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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.

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Section: Introductionmentioning

confidence: 99%

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

Meng

2018

Complexity

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“…On the one hand, because quaternion-valued neural networks (QVNNs) as an extension of the real-valued neural networks and complex-valued neural networks can be extensively applied to the fields of robotics, attitude control of satellites, computer graphics, ensemble control, color night vision, and image compression ( [12][13][14]) and one of the benefits by using quaternion is the three-dimensional geometrical affine transformation that can be represented efficiently and compactly, the study of dynamical behaviors for QVNNs has received much attention of many scholars and some good results have been obtained for the stability [15][16][17][18][19], dissipativity [20], periodicity [21], pseduo almost periodicity [22], and synchronization of QVNNs [23,24].…”

Section: Introductionmentioning

confidence: 99%

Anti-Periodic Dynamics of Quaternion-Valued Fuzzy Cellular Neural Networks with Time-Varying Delays on Time Scales

Shen

2018

Discrete Dynamics in Nature and Society

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A class of quaternion-valued fuzzy cellular neural networks with time-varying delays on time scales is proposed. Based on inequality analysis techniques on time scales, a fixed point theorem and the theory of calculus on time scales, the existence, and global exponential stability of anti-periodic solutions for this class of neural networks are established. The obtained results are completely new and supplement to the known results. Finally, a numerical example is given to illustrate the feasibility of our results.

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“…The complex‐valued neural networks as an extension of real‐valued neural networks, which use complex‐valued states, connection weights, or activation functions have become a hot topic of neural networks. Therefore, there have been increasing research interests in the dynamical behaviors of complex‐valued recurrent neural networks, see and references therein. Recently, Chen, Song, Zhao and Liu considered the complex‐valued neural networks with leakage delay and mixed delays described by an on linear difference equation of the form

\begin{matrix} right & left z_{i} (k + 1) = a_{i} z_{i} (k - δ) + \sum_{j = 1}^{n} b_{i j} f_{j} (z_{j} (k)) & right \\ right & left + \sum_{j = 1}^{n} d_{i j} \sum_{l = 1}^{\infty} f_{j} (z_{j} (k - l)) + I_{i}, i = 1, 2, \dots, n . \end{matrix}

Zhang and Yu investigated a class of complex‐valued Cohen‐Grossberg neural networks with time delays

z^{'} (t) = - a z (t) [h (z (t)) - A f (z (t)) - B g (z (t - τ)) - u] .

In , Song et al.…”

Section: Introductionmentioning

confidence: 99%

“…The complex-valued neural networks as an extension of real-valued neural networks, which use complex-valued states, connection weights, or activation functions have become a hot topic of neural networks. Therefore, there have been increasing research interests in the dynamical behaviors of complex-valued recurrent neural networks, see [1][2][3] and references therein. Recently, Chen, Song, Zhao and Liu [4] considered the complex-valued neural networks with leakage delay and mixed delays described by an on linear difference equation of the form…”

Section: Introductionmentioning

confidence: 99%

Stability Analysis of Periodic Solution for a Complex‐valued Neural Networks With Bounded and Unbounded Delays

2017

Asian Journal of Control

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This paper is devoted to investigating a class of complex‐valued neural networks with bounded and unbounded delays. By means of Mawhin's continuation theorem, some criteria on existence and uniqueness of periodic solution are established for the complex‐valued neural networks. By constructing an appropriate Lyapunov‐Krasovskii functional and M−matrix theory, some sufficient conditions are derived for the global exponential stability of periodic solutions to the complex‐valued neural networks. Finally, two numerical examples are given to show the effectiveness and merits of the present results.

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Global μ-stability criteria for quaternion-valued neural networks with unbounded time-varying delays

Cited by 168 publications

References 39 publications

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

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

Anti-Periodic Dynamics of Quaternion-Valued Fuzzy Cellular Neural Networks with Time-Varying Delays on Time Scales

Stability Analysis of Periodic Solution for a Complex‐valued Neural Networks With Bounded and Unbounded Delays

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