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

Xiang, Jianglian

doi:10.1002/mma.6363

Cited by 14 publications

(5 citation statements)

References 25 publications

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“…The global stability of QVNNs with time‐varying delays has been investigated in Liu et al 19 By virtue of the Lyapunov function method, some sufficient criteria were derived to ensure the global

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‐stability of delayed QVNNs. Some more interesting results of QVNNs with a variety of delays were discussed in previous studies 20–24 …”

Section: Introductionmentioning

confidence: 81%

“…Some more interesting results of QVNNs with a variety of delays were discussed in previous studies. [20][21][22][23][24] We are well aware that the number of stable equilibrium points of NNs is of great importance for their practical applications. Based on the number of stable equilibrium points, the stability of NNs can be divided into two categories.…”

Section: Introductionmentioning

confidence: 99%

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Multipleμ‐stability analysis of time‐varying delayed quaternion‐valued neural networks

Chouhan

Das

Singh

et al. 2023

Math Methods in App Sciences

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This article addresses the multiple 𝜇-stability analysis of n-dimensional quaternion-valued neural networks (QVNNs) with unbounded time-varying delays (UTVD) and two general classes of activation functions (AFs). Firstly, the QVNNs are decomposed into four equivalent real-valued systems, and based on the geometrical configuration of the AFs, the state space H n is divided into 3 4n disjoint regions. Considering the properties of AFs, several sufficient conditions are derived to ensure the coexistence of 3 4n equilibria, out of which 2 4n are locally 𝜇-stable. Moreover, some sufficient conditions for multiple exponential stability, multiple power stability, and multiple log stability are also derived in this article.Finally, two numerical examples are presented. The first example validates the effectiveness of the proposed theoretical results while the second example illustrates the application of QVNNs on the associative memory, which shows that QVNNs have the ability to reliably retrieve true-color image patterns.

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\mu

‐stability of delayed QVNNs. Some more interesting results of QVNNs with a variety of delays were discussed in previous studies 20–24 …”

Section: Introductionmentioning

confidence: 81%

Section: Introductionmentioning

confidence: 99%

Multipleμ‐stability analysis of time‐varying delayed quaternion‐valued neural networks

Chouhan

Das

Singh

et al. 2023

Math Methods in App Sciences

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“…The prevalence of quaternion neural network (QNN) theory is uninterruptedly enhanced of late years 5–7 . Quaternion has a real part and three imaginary parts, so QNNs combine many advantages of real‐valued neural networks or complex‐valued neural networks; besides, QNNs also have some features that they do not have, such as processing high‐dimensional data and two‐ or three‐dimensional space affine transformation.…”

Section: Introductionmentioning

confidence: 99%

“…4 The prevalence of quaternion neural network (QNN) theory is uninterruptedly enhanced of late years. [5][6][7] Quaternion has a real part and three imaginary parts, so QNNs combine many advantages of real-valued neural networks or complex-valued neural networks; besides, QNNs also have some features that they do not have, such as processing high-dimensional data and two-or three-dimensional space affine transformation. QNNs are extensively applied in practical fields, like human motion modeling, 8 sensor fusion, 9 spacecraft attitude tracking, 10 and image encryption 11 ; therefore, it is of significant theoretical meaning and realistic worth to consider the characteristics.…”

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confidence: 99%

A direct analysis method to state bounding for high‐order quaternion Hopfield neural networks with mixed delays and bounded disturbances

Chen

Xue

Zhang

2023

Math Methods in App Sciences

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The main research in this paper is the state bounding problem of high-order quaternion Hopfield neural networks (HOQHNNs) with time-varying discrete delays, unbounded distributed delays, and bounded disturbances. In the research process, firstly, the considered HOQHNNs are decomposed into four equivalent real-valued Hopfield neural networks (RHNNs) to solve the problem that quaternion multiplication is not commutative, and then, a sufficient condition related to time delays is given to ensure that the state trajectories that are contained in or globally exponentially convergent into a cuboid. Thereby, the corresponding reachable set estimation is obtained. Numerical examples are provided to illustrate validity of theoretical results. At present, the research on HOQHNNs with mixed time delays adopts Lyapunov-Krasovskii functional (LKF) method, which needs to not only choose the appropriate LKF but also take into account both conservatism and computational complexity. Besides, there is no literature to study the state bounding of HOQHNNs with mixed delays.The method suggested in the present text has three merits: (1) According to the definition of state bounding straightway, it has no use any LKF, which avoids massive calculations and solutions of high-dimensional matrix inequalities; (2) it is available not only to HOQHNNs but also to RHNNs and complex-valued Hopfield neural networks (CHNNs); and (3) make up for the blank of state bounding research of HOQHNNs. KEYWORDS direct analysis method, quaternion Hopfield neural networks, reachable set estimation, state bounding, unbounded distributed delays MSC CLASSIFICATION 93D20 INTRODUCTIONWith the intensive study of human brain, various deep learning technologies have been paid more and more attention, especially neural networks that belong to the category of artificial intelligence. The research of neural networks plays an important role in modern engineering and electronics. The Hopfield neural network was first developed in 1982. 1 It is a

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“…From the Lyapunov functional method and some inequality techniques, Luo, Jiang and Wang [14] studied the anti-periodic solutions of a Clifford-valued high-order neural network with proportional lags. The almost periodic solution problem for a quaternion-valued neural networks has been investigated by Li and Xiang [15]. For more results for high-dimensional dynamic systems and networks systems, please see, e.g., references [16][17][18][19][20] and related references.…”

Section: Introductionmentioning

confidence: 99%

Periodic Solution Problems for a Class of Hebbian-Type Networks with Time-Varying Delays

Xu,

Yin,

2023

Symmetry

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By using Gronwall’s inequality and coincidence degree theory, the sufficient conditions of the globally exponential stability and existence are given for a Hebbian-type network with time-varying delays. The periodic behavior phenomenon is one of the hot topics in network systems research, from which we can discover the symmetric characteristics of certain neurons. The main theorems in the present paper are illustrated using a numerical example.

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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

Cited by 14 publications

References 25 publications

Multipleμ‐stability analysis of time‐varying delayed quaternion‐valued neural networks

Multipleμ‐stability analysis of time‐varying delayed quaternion‐valued neural networks

A direct analysis method to state bounding for high‐order quaternion Hopfield neural networks with mixed delays and bounded disturbances

Periodic Solution Problems for a Class of Hebbian-Type Networks with Time-Varying Delays

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