A direct analysis method to Lagrangian global exponential stability for quaternion memristive neural networks with mixed delays

Chen, Yonghui; Xue, Yuncan; Yang, Xiaona; Zhang, Xian

doi:10.1016/j.amc.2022.127633

Cited by 11 publications

(6 citation statements)

References 27 publications

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“…In addition, compared with real-valued and complex-valued NNs, some superior performance of quaternion NNs have been found such as high-efficiency and general representation [18]. So, the study on quaternion NNs has become one of hot topics in many fields [5,[19][20][21][22]. Recently, some scholars have established stability criteria of quaternion NNs, including exponential stability [21], global robust exponential stability [22,23], and Lagrangian global exponential stability (GES) [19].…”

Section: Introductionmentioning

confidence: 99%

“…So, the study on quaternion NNs has become one of hot topics in many fields [5,[19][20][21][22]. Recently, some scholars have established stability criteria of quaternion NNs, including exponential stability [21], global robust exponential stability [22,23], and Lagrangian global exponential stability (GES) [19]. Several exponential stability criteria are derived by using the Lyapunov-Krasovskii functional (LKF) method, the system decomposition method, and the linear matrix inequality (LMI) method [21].…”

Section: Introductionmentioning

confidence: 99%

“…By establishing a quaternion matrix differential inequality and applying algebraic graph theory and iterative method, several global robust exponential stability criteria are given [22]. For a class of quaternion NNs with leakage delays, unbounded distributed delays, and time-varying discrete transmission delays, instead of the traditional system decomposition method, LMI method, and LKF method, the authors propose a system solution-based method that takes the quaternion NNs as a whole in the process of establishing Lagrangian GES criterion [19]. Exponential stability criteria of discrete-time quaternion NNs affected multiple delays have been obtained in [24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Global exponential stability of quaternion bidirectional associative memory neural networks with multiple delays

Zhang,

Liang,

Lan

et al. 2024

Math Methods in App Sciences

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In this paper, the global exponential stability of quaternion BAM neural networks with mixed delays is investigated. The involved delays include multiple time‐varying transmission delays and unbounded distributed delays. Existence and uniqueness of equilibrium point of the considered neural networks are investigated by using the homeomorphism theory between topology spaces. To show sufficient conditions for global exponential stability of the unique equilibrium point, a method based on estimation of solutions is presented. The acquired stability conditions contain only several simple linear scalar inequalities, which can be easily solved. The availability of theoretical results is shown by a numerical example. A point worth emphasizing is that the method based on estimation of solutions is applicable for models of many time‐delay systems after a minor modification.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Global exponential stability of quaternion bidirectional associative memory neural networks with multiple delays

Zhang,

Liang,

Lan

et al. 2024

Math Methods in App Sciences

Self Cite

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“…The effect of time delays on the system has been paid close attention in the fields of modern practical engineering and control theory. As we all know, time delay is the main factor that makes the system divergent, chaotic, and unstable 21–27 . Moreover, because of extensive parallel ways with various lengths and synapses with various sizes, neural networks generally have spatial characteristics.…”

Section: Introductionmentioning

confidence: 99%

“…As we all know, time delay is the main factor that makes the system divergent, chaotic, and unstable. [21][22][23][24][25][26][27] Moreover, because of extensive parallel ways with various lengths and synapses with various sizes, neural networks generally have spatial characteristics. Therefore, it is hoped to introduce distributed delay into the model of neural networks, so that the influence of delays on the state is cumulative.…”

mentioning

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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Lagrange stability and passivity in the mean square sense of discrete-time stochastic Markovian switched neural networks with time-varying mixed delays

Yang,

Ma,

Wang

2024

Applied Mathematics and Computation

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A direct analysis method to Lagrangian global exponential stability for quaternion memristive neural networks with mixed delays

Cited by 11 publications

References 27 publications

Global exponential stability of quaternion bidirectional associative memory neural networks with multiple delays

Global exponential stability of quaternion bidirectional associative memory neural networks with multiple delays

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

Lagrange stability and passivity in the mean square sense of discrete-time stochastic Markovian switched neural networks with time-varying mixed delays

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