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Wu X, Tu Z, Peng T, Wang D. Global attractive set for quaternion-valued neural networks with neutral items. Sci Rep 2024; 14:17975. [PMID: 39095525 PMCID: PMC11297258 DOI: 10.1038/s41598-024-68763-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/02/2024] [Accepted: 07/27/2024] [Indexed: 08/04/2024] Open
Abstract
This paper investigated the global attractive set for quaternion-valued neural networks (QVNNs) with leakage delay, time-varying delay, and neutral items. Based on various basic conditions of activation function, the global attractive set and global exponential attractive set of QVNNs are given combined with novel analytical techniques and Lyapunov theory. The QVNNs are studied by a direct method, without any decomposition. The time delay can be non-differential, which makes the results more pragmatic. Restrictions on the activation function of the neutral item are relaxed. The neutral activation function can be bounded or unbounded, which makes the results more practical. Two simulation examples are given to verify the validity of the theory results.
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Affiliation(s)
- Xili Wu
- School of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou, 404100, China
| | - Zhengwen Tu
- School of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou, 404100, China.
| | - Tao Peng
- School of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou, 404100, China
| | - Dandan Wang
- School of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou, 404100, China
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2
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Akca H, Aouiti C, Touati F, Xu C. Finite-time passivity of neutral-type complex-valued neural networks with time-varying delays. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2024; 21:6097-6122. [PMID: 38872571 DOI: 10.3934/mbe.2024268] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2024]
Abstract
In this work, we investigated the finite-time passivity problem of neutral-type complex-valued neural networks with time-varying delays. On the basis of the Lyapunov functional, Wirtinger-type inequality technique, and linear matrix inequalities (LMIs) approach, new sufficient conditions were derived to ensure the finite-time boundedness (FTB) and finite-time passivity (FTP) of the concerned network model. At last, two numerical examples with simulations were presented to demonstrate the validity of our criteria.
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Affiliation(s)
- Haydar Akca
- Abu Dhabi University, College of Arts and Sciences, Department of Applied Sciences and Mathematics, Abu Dhabi, UAE
| | - Chaouki Aouiti
- University Carthage, Faculty of Sciences of Bizerta, Department of Mathematics, GAMA Laboratory LR21ES10, BP W, 7021 Zarzouna, Bizerta, Tunisia
| | - Farid Touati
- University Carthage, Faculty of Sciences of Bizerta, Department of Mathematics, GAMA Laboratory LR21ES10, BP W, 7021 Zarzouna, Bizerta, Tunisia
| | - Changjin Xu
- Guizhou Key Laboratory of Economics System Simulation, Guizhou University of Finance and Economics, Guiyang 550004, China
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3
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Tan G, Wang Z, Shi Z. Proportional-Integral State Estimator for Quaternion-Valued Neural Networks With Time-Varying Delays. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2023; 34:1074-1079. [PMID: 34424846 DOI: 10.1109/tnnls.2021.3103979] [Citation(s) in RCA: 13] [Impact Index Per Article: 13.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
This brief investigates the problem of state estimation of quaternion-valued neural networks (QVNNs) with time-varying delays. First, by extending the Jensen inequality to quaternion domain, an extended Jensen inequality with quaternion term is derived. Second, a class of proportional-integral state estimator (PISE) with exponential decay term is proposed. Then, by constructing a suitable Lyapunov-Krasovskii functional (LKF), some sufficient conditions are obtained to ensure the existence of the designed PISE and the gain matrices of the designed PISE can be directly computed. Simulations are given to illustrate the advantage of the proposed method.
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4
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Topology Identification of Time-Scales Complex Networks. MATHEMATICS 2022. [DOI: 10.3390/math10101755] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/04/2022]
Abstract
This paper studies a topology identification problem of complex networks with dynamics on different time scales. Using the adaptive synchronization method, some criteria for a successful estimation are obtained. In particular, by regulating the original network to synchronize with an auxiliary chaotic network, this work further explores a way to avoid the precondition of linear independence. When the adaptive controller fails to achieve the outer synchronization, an impulsive control method is used. In the end, we conclude with three numerical simulations. The results obtained in this paper generalize continuous, discrete with arbitrary time step size and mixed cases.
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Li J, Wang Z, Dong H, Ghinea G. Outlier-Resistant Remote State Estimation for Recurrent Neural Networks With Mixed Time-Delays. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2021; 32:2266-2273. [PMID: 32452774 DOI: 10.1109/tnnls.2020.2991151] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
In this brief, a new outlier-resistant state estimation (SE) problem is addressed for a class of recurrent neural networks (RNNs) with mixed time-delays. The mixed time delays comprise both discrete and distributed delays that occur frequently in signal transmissions among artificial neurons. Measurement outputs are sometimes subject to abnormal disturbances (resulting probably from sensor aging/outages/faults/failures and unpredictable environmental changes) leading to measurement outliers that would deteriorate the estimation performance if directly taken into the innovation in the estimator design. We propose to use a certain confidence-dependent saturation function to mitigate the side effects from the measurement outliers on the estimation error dynamics (EEDs). Through using a combination of Lyapunov-Krasovskii functional and inequality manipulations, a delay-dependent criterion is established for the existence of the outlier-resistant state estimator ensuring that the corresponding EED achieves the asymptotic stability with a prescribed H∞ performance index. Then, the explicit characterization of the estimator gain is obtained by solving a convex optimization problem. Finally, numerical simulation is carried out to demonstrate the usefulness of the derived theoretical results.
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6
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Li Q, Liang J, Qu H. H ∞ estimation for stochastic semi-Markovian switching CVNNs with missing measurements and mode-dependent delays. Neural Netw 2021; 141:281-293. [PMID: 33933888 DOI: 10.1016/j.neunet.2021.04.022] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/02/2020] [Revised: 04/15/2021] [Accepted: 04/15/2021] [Indexed: 10/21/2022]
Abstract
This article is devoted to the H∞ estimation problem for stochastic semi-Markovian switching complex-valued neural networks subject to incomplete measurement outputs, where the time-varying delay also depends on another semi-Markov process. A sequence of random variables with known statistical property is introduced to depict the missing measurement phenomenon. Based on the generalized Itoˆ's formula in complex form concerning with the semi-Markovian systems, complex-valued reciprocal convex inequality as well as intensive stochastic analysis method, some mode-dependent sufficient conditions are presented guaranteeing the estimation error system to be exponentially mean-square stable with a prespecified H∞ disturbance attenuation level. In addition, the mode-dependent estimator gain matrices are appropriately designed according to the feasible solutions of certain complex matrix inequalities. In the end, one numerical example is provided to illustrate effectiveness of the theoretical results.
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Affiliation(s)
- Qiang Li
- School of Mathematics, Southeast University, Nanjing 210096, China.
| | - Jinling Liang
- School of Mathematics, Southeast University, Nanjing 210096, China.
| | - Hong Qu
- School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China.
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7
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Robust Passivity and Stability Analysis of Uncertain Complex-Valued Impulsive Neural Networks with Time-Varying Delays. Neural Process Lett 2021. [DOI: 10.1007/s11063-020-10401-w] [Citation(s) in RCA: 23] [Impact Index Per Article: 7.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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8
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Global exponential stability of delayed complex-valued neural networks with discontinuous activation functions. Neurocomputing 2020. [DOI: 10.1016/j.neucom.2020.02.006] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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9
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Ganesan S, Gnaneswaran N. State-Feedback Filtering for Delayed Discrete-Time Complex-Valued Neural Networks. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2020; 31:4726-4736. [PMID: 31905153 DOI: 10.1109/tnnls.2019.2957304] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
This article explores a new filtering problem for the class of delayed discrete-time complex-valued neural networks (CVNNs) via state-feedback control design. The novelty of this article comes from the consideration of the newly developed complex-valued reciprocal convex matrix inequality as well as the complex-valued Jensen-based summation inequalities (JSIs). By employing an appropriate Lyapunov-Krasovskii functional (LKF) and by using newly proposed complex-valued inequalities, attention is concentrated on the design of a state-feedback filter such that the associated filtering error system is asymptotically stable with prescribed filter and control gain matrices. The proposed theoretical results are presented in terms of complex-valued linear matrix inequalities (LMIs) that can be solved numerically by using the YALMIP toolbox in MATLAB software. Additionally, one numerical example is given to confirm the validity of the resulting sufficient conditions with the availability of the suitable control and filter design.
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10
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Improved Stabilization Results for Markovian Switching CVNNs with Partly Unknown Transition Rates. Neural Process Lett 2020. [DOI: 10.1007/s11063-020-10299-4] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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11
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12
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Robust Dissipativity Analysis of Hopfield-Type Complex-Valued Neural Networks with Time-Varying Delays and Linear Fractional Uncertainties. MATHEMATICS 2020. [DOI: 10.3390/math8040595] [Citation(s) in RCA: 33] [Impact Index Per Article: 8.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
We study the robust dissipativity issue with respect to the Hopfield-type of complex-valued neural network (HTCVNN) models incorporated with time-varying delays and linear fractional uncertainties. To avoid the computational issues in the complex domain, we divide the original complex-valued system into two real-valued systems. We devise an appropriate Lyapunov-Krasovskii functional (LKF) equipped with general integral terms to facilitate the analysis. By exploiting the multiple integral inequality method, the sufficient conditions for the dissipativity of HTCVNN models are obtained via the linear matrix inequalities (LMIs). The MATLAB software package is used to solve the LMIs effectively. We devise a number of numerical models and their empirical results positively ascertain the obtained results.
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13
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Gao Y, Zhu S, Li J. Reachable set bounding for a class of memristive complex-valued neural networks with disturbances. Neurocomputing 2020. [DOI: 10.1016/j.neucom.2019.12.085] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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14
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Robust Exponential Stability for Discrete-Time Quaternion-Valued Neural Networks with Time Delays and Parameter Uncertainties. Neural Process Lett 2020. [DOI: 10.1007/s11063-020-10196-w] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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15
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Li N, Zheng WX. Passivity Analysis for Quaternion-Valued Memristor-Based Neural Networks With Time-Varying Delay. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2020; 31:639-650. [PMID: 31021808 DOI: 10.1109/tnnls.2019.2908755] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
This paper is concerned with the problem of global exponential passivity for quaternion-valued memristor-based neural networks (QVMNNs) with time-varying delay. The QVMNNs can be seen as a switched system due to the memristor parameters are switching according to the states of the network. This is the first time that the global exponential passivity of QVMNNs with time-varying delay is investigated. By means of a nondecomposition method and structuring novel Lyapunov functional in form of quaternion self-conjugate matrices, the delay-dependent passivity criteria are derived in the forms of quaternion-valued linear matrix inequalities (LMIs) as well as complex-valued LMIs. Furthermore, the asymptotical stability criteria can be obtained from the proposed passivity criteria. Finally, a numerical example is presented to illustrate the effectiveness of the theoretical results.
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16
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Global µ-stability of neutral-type impulsive complex-valued BAM neural networks with leakage delay and unbounded time-varying delays. Neurocomputing 2020. [DOI: 10.1016/j.neucom.2019.09.008] [Citation(s) in RCA: 21] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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17
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Wang X, Wang Z, Song Q, Shen H, Huang X. A waiting-time-based event-triggered scheme for stabilization of complex-valued neural networks. Neural Netw 2020; 121:329-338. [DOI: 10.1016/j.neunet.2019.09.032] [Citation(s) in RCA: 34] [Impact Index Per Article: 8.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/25/2019] [Revised: 09/11/2019] [Accepted: 09/22/2019] [Indexed: 10/25/2022]
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18
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Gunasekaran N, Zhai G. Stability analysis for uncertain switched delayed complex-valued neural networks. Neurocomputing 2019. [DOI: 10.1016/j.neucom.2019.08.030] [Citation(s) in RCA: 21] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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19
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20
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Exponential Stability and Sampled-Data Synchronization of Delayed Complex-Valued Memristive Neural Networks. Neural Process Lett 2019. [DOI: 10.1007/s11063-019-10082-0] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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21
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Jmal A, Ben Makhlouf A, Nagy AM, Naifar O. Finite-Time Stability for Caputo–Katugampola Fractional-Order Time-Delayed Neural Networks. Neural Process Lett 2019. [DOI: 10.1007/s11063-019-10060-6] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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22
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Samidurai R, Sriraman R, Zhu S. Leakage delay-dependent stability analysis for complex-valued neural networks with discrete and distributed time-varying delays. Neurocomputing 2019. [DOI: 10.1016/j.neucom.2019.02.027] [Citation(s) in RCA: 36] [Impact Index Per Article: 7.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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23
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Hou P, Hu J, Gao J, Zhu P. Stability Analysis for Memristor-Based Complex-Valued Neural Networks with Time Delays. ENTROPY (BASEL, SWITZERLAND) 2019; 21:e21020120. [PMID: 33266836 PMCID: PMC7514603 DOI: 10.3390/e21020120] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/06/2018] [Revised: 01/19/2019] [Accepted: 01/21/2019] [Indexed: 06/12/2023]
Abstract
In this paper, the problem of stability analysis for memristor-based complex-valued neural networks (MCVNNs) with time-varying delays is investigated extensively. This paper focuses on the exponential stability of the MCVNNs with time-varying delays. By means of the Brouwer's fixed-point theorem and M-matrix, the existence, uniqueness, and exponential stability of the equilibrium point for MCVNNs are studied, and several sufficient conditions are obtained. In particular, these results can be applied to general MCVNNs whether the activation functions could be explicitly described by dividing into two parts of the real parts and imaginary parts or not. Two numerical simulation examples are provided to illustrate the effectiveness of the theoretical results.
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Affiliation(s)
- Ping Hou
- School of Management, Nanjing University of Posts and Telecommunications, Nanjing 210023, China
| | - Jun Hu
- School of Management Science and Engineering, Central University of Finance and Economics, Beijing 100080, China
| | - Jie Gao
- School of Sciences, Southwest Petroleum University, Chengdu 610500, China
| | - Peican Zhu
- School of Computer Science, Northwestern Polytechnical University, Xi’an 710072, China
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24
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Stability Analysis of Quaternion-Valued Neutral-Type Neural Networks with Time-Varying Delay. MATHEMATICS 2019. [DOI: 10.3390/math7010101] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
This paper addresses the problem of global μ -stability for quaternion-valued neutral-type neural networks (QVNTNNs) with time-varying delays. First, QVNTNNs are transformed into two complex-valued systems by using a transformation to reduce the complexity of the computation generated by the non-commutativity of quaternion multiplication. A new convex inequality in a complex field is introduced. In what follows, the condition for the existence and uniqueness of the equilibrium point is primarily obtained by the homeomorphism theory. Next, the global stability conditions of the complex-valued systems are provided by constructing a novel Lyapunov–Krasovskii functional, using an integral inequality technique, and reciprocal convex combination approach. The gained global μ -stability conditions can be divided into three different kinds of stability forms by varying the positive continuous function μ ( t ) . Finally, three reliable examples and a simulation are given to display the effectiveness of the proposed methods.
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25
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Li N, Cao J. Global dissipativity analysis of quaternion-valued memristor-based neural networks with proportional delay. Neurocomputing 2018. [DOI: 10.1016/j.neucom.2018.09.030] [Citation(s) in RCA: 33] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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26
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Aouiti C, Assali EA. Stability Analysis for a Class of Impulsive Bidirectional Associative Memory (BAM) Neural Networks with Distributed Delays and Leakage Time-Varying Delays. Neural Process Lett 2018. [DOI: 10.1007/s11063-018-9937-y] [Citation(s) in RCA: 25] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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27
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Song Q, Chen X. Multistability Analysis of Quaternion-Valued Neural Networks With Time Delays. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2018; 29:5430-5440. [PMID: 29994739 DOI: 10.1109/tnnls.2018.2801297] [Citation(s) in RCA: 69] [Impact Index Per Article: 11.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
This paper addresses the multistability issue for quaternion-valued neural networks (QVNNs) with time delays. By using the inequality technique, sufficient conditions are proposed for the boundedness and the global attractivity of delayed QVNNs. Based on the geometrical properties of the activation functions, several criteria are obtained to ensure the existence of equilibrium points, of which are locally stable. Two numerical examples are provided to illustrate the effectiveness of the obtained results.
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28
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Popa CA. Global exponential stability of neutral-type octonion-valued neural networks with time-varying delays. Neurocomputing 2018. [DOI: 10.1016/j.neucom.2018.05.004] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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29
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30
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Global Mittag-Leffler stability and synchronization analysis of fractional-order quaternion-valued neural networks with linear threshold neurons. Neural Netw 2018; 105:88-103. [DOI: 10.1016/j.neunet.2018.04.015] [Citation(s) in RCA: 89] [Impact Index Per Article: 14.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/15/2017] [Revised: 02/12/2018] [Accepted: 04/20/2018] [Indexed: 11/15/2022]
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31
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Global exponential stability of octonion-valued neural networks with leakage delay and mixed delays. Neural Netw 2018; 105:277-293. [DOI: 10.1016/j.neunet.2018.05.006] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/19/2017] [Revised: 03/12/2018] [Accepted: 05/04/2018] [Indexed: 11/19/2022]
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32
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Aouiti C, Assali EA. Stability analysis for a class of impulsive high-order Hopfield neural networks with leakage time-varying delays. Neural Comput Appl 2018. [DOI: 10.1007/s00521-018-3585-z] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023]
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33
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Chen X, Song Q, Li Z, Zhao Z, Liu Y. Stability Analysis of Continuous-Time and Discrete-Time Quaternion-Valued Neural Networks With Linear Threshold Neurons. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2018; 29:2769-2781. [PMID: 28600263 DOI: 10.1109/tnnls.2017.2704286] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
This paper addresses the problem of stability for continuous-time and discrete-time quaternion-valued neural networks (QVNNs) with linear threshold neurons. Applying the semidiscretization technique to the continuous-time QVNNs, the discrete-time analogs are obtained, which preserve the dynamical characteristics of their continuous-time counterparts. Via the plural decomposition method of quaternion, homeomorphic mapping theorem, as well as Lyapunov theorem, some sufficient conditions on the existence, uniqueness, and global asymptotical stability of the equilibrium point are derived for the continuous-time QVNNs and their discrete-time analogs, respectively. Furthermore, a uniform sufficient condition on the existence, uniqueness, and global asymptotical stability of the equilibrium point is obtained for both continuous-time QVNNs and their discrete-time version. Finally, two numerical examples are provided to substantiate the effectiveness of the proposed results.
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34
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35
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Synchronization Criterion of Complex Dynamical Networks with Both Leakage Delay and Coupling Delay on Time Scales. Neural Process Lett 2018. [DOI: 10.1007/s11063-018-9821-9] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
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36
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Global Mittag-Leffler Boundedness for Fractional-Order Complex-Valued Cohen–Grossberg Neural Networks. Neural Process Lett 2018. [DOI: 10.1007/s11063-018-9790-z] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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37
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Song Q, Yu Q, Zhao Z, Liu Y, Alsaadi FE. Dynamics of complex-valued neural networks with variable coefficients and proportional delays. Neurocomputing 2018. [DOI: 10.1016/j.neucom.2017.11.041] [Citation(s) in RCA: 33] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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38
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Boundedness and periodicity for linear threshold discrete-time quaternion-valued neural network with time-delays. Neurocomputing 2017. [DOI: 10.1016/j.neucom.2017.06.047] [Citation(s) in RCA: 47] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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39
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Global Asymptotic Stability for Complex-Valued Neural Networks with Time-Varying Delays via New Lyapunov Functionals and Complex-Valued Inequalities. Neural Process Lett 2017. [DOI: 10.1007/s11063-017-9757-5] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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40
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The Global Exponential Stability of the Delayed Complex-Valued Neural Networks with Almost Periodic Coefficients and Discontinuous Activations. Neural Process Lett 2017. [DOI: 10.1007/s11063-017-9736-x] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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41
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Liu D, Zhu S, Ye E. Synchronization stability of memristor-based complex-valued neural networks with time delays. Neural Netw 2017; 96:115-127. [PMID: 28987975 DOI: 10.1016/j.neunet.2017.09.008] [Citation(s) in RCA: 40] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/16/2017] [Revised: 08/30/2017] [Accepted: 09/01/2017] [Indexed: 11/16/2022]
Abstract
This paper focuses on the dynamical property of a class of memristor-based complex-valued neural networks (MCVNNs) with time delays. By constructing the appropriate Lyapunov functional and utilizing the inequality technique, sufficient conditions are proposed to guarantee exponential synchronization of the coupled systems based on drive-response concept. The proposed results are very easy to verify, and they also extend some previous related works on memristor-based real-valued neural networks. Meanwhile, the obtained sufficient conditions of this paper may be conducive to qualitative analysis of some complex-valued nonlinear delayed systems. A numerical example is given to demonstrate the effectiveness of our theoretical results.
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Affiliation(s)
- Dan Liu
- School of Mathematics, China University of Mining and Technology, Xuzhou, 221116, China
| | - Song Zhu
- School of Mathematics, China University of Mining and Technology, Xuzhou, 221116, China.
| | - Er Ye
- School of Mathematics, Southeast University, Nanjing 210096, China
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42
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Tan Y, Tang S, Yang J, Liu Z. Robust stability analysis of impulsive complex-valued neural networks with time delays and parameter uncertainties. JOURNAL OF INEQUALITIES AND APPLICATIONS 2017; 2017:215. [PMID: 28959116 PMCID: PMC5594064 DOI: 10.1186/s13660-017-1490-0] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 06/07/2017] [Accepted: 08/27/2017] [Indexed: 06/07/2023]
Abstract
The present study considers the robust stability for impulsive complex-valued neural networks (CVNNs) with discrete time delays. By applying the homeomorphic mapping theorem and some inequalities in a complex domain, some sufficient conditions are obtained to prove the existence and uniqueness of the equilibrium for the CVNNs. By constructing appropriate Lyapunov-Krasovskii functionals and employing the complex-valued matrix inequality skills, the study finds the conditions to guarantee its global robust stability. A numerical simulation illustrates the correctness of the proposed theoretical results.
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Affiliation(s)
- Yuanshun Tan
- College of Mathematics and Statistics, Chongqing Jiaotong University, Chongqing, 400074 China
| | - Sanyi Tang
- College of Mathematics and Statistics, Shaanxi Normal University, Shanxi, 710062 China
| | - Jin Yang
- College of Mathematics and Statistics, Chongqing Jiaotong University, Chongqing, 400074 China
| | - Zijian Liu
- College of Mathematics and Statistics, Chongqing Jiaotong University, Chongqing, 400074 China
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Zhang Z, Liu X, Chen J, Guo R, Zhou S. Further stability analysis for delayed complex-valued recurrent neural networks. Neurocomputing 2017. [DOI: 10.1016/j.neucom.2017.04.013] [Citation(s) in RCA: 33] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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44
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Chen X, Li Z, Song Q, Hu J, Tan Y. Robust stability analysis of quaternion-valued neural networks with time delays and parameter uncertainties. Neural Netw 2017; 91:55-65. [DOI: 10.1016/j.neunet.2017.04.006] [Citation(s) in RCA: 111] [Impact Index Per Article: 15.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/01/2016] [Revised: 02/17/2017] [Accepted: 04/14/2017] [Indexed: 11/30/2022]
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45
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Finite-time stability analysis of fractional-order complex-valued memristor-based neural networks with both leakage and time-varying delays. Neurocomputing 2017. [DOI: 10.1016/j.neucom.2017.03.042] [Citation(s) in RCA: 81] [Impact Index Per Article: 11.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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46
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Shu H, Song Q, Liu Y, Zhao Z, Alsaadi FE. Globalμ−stability of quaternion-valued neural networks with non-differentiable time-varying delays. Neurocomputing 2017. [DOI: 10.1016/j.neucom.2017.03.052] [Citation(s) in RCA: 69] [Impact Index Per Article: 9.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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47
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Subramanian K, Muthukumar P. Global asymptotic stability of complex-valued neural networks with additive time-varying delays. Cogn Neurodyn 2017; 11:293-306. [PMID: 28559957 DOI: 10.1007/s11571-017-9429-1] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/28/2016] [Revised: 02/15/2017] [Accepted: 03/06/2017] [Indexed: 05/29/2023] Open
Abstract
In this paper, we extensively study the global asymptotic stability problem of complex-valued neural networks with leakage delay and additive time-varying delays. By constructing a suitable Lyapunov-Krasovskii functional and applying newly developed complex valued integral inequalities, sufficient conditions for the global asymptotic stability of proposed neural networks are established in the form of complex-valued linear matrix inequalities. This linear matrix inequalities are efficiently solved by using standard available numerical packages. Finally, three numerical examples are given to demonstrate the effectiveness of the theoretical results.
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Affiliation(s)
- K Subramanian
- Department of Mathematics, The Gandhigram Rural Institute - Deemed University, Gandhigram, Tamilnadu 624 302 India
| | - P Muthukumar
- Department of Mathematics, The Gandhigram Rural Institute - Deemed University, Gandhigram, Tamilnadu 624 302 India
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48
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Almost periodic dynamics of the delayed complex-valued recurrent neural networks with discontinuous activation functions. Neural Comput Appl 2017. [DOI: 10.1007/s00521-017-2911-1] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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50
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Hu J, Zeng C. Adaptive exponential synchronization of complex-valued Cohen–Grossberg neural networks with known and unknown parameters. Neural Netw 2017; 86:90-101. [DOI: 10.1016/j.neunet.2016.11.001] [Citation(s) in RCA: 54] [Impact Index Per Article: 7.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/08/2016] [Revised: 09/24/2016] [Accepted: 11/04/2016] [Indexed: 11/25/2022]
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