1
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Fixed-Time Synchronization for Delayed Quaternion-Valued Stochastic Fuzzy Neural Network with Reaction–Diffusion Terms. Neural Process Lett 2022. [DOI: 10.1007/s11063-022-10871-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/16/2022]
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2
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Chouhan SS, kumar R, Sarkar S, Das S. Multistability Analysis of Octonion-Valued Neural Networks with Time-Varying Delays. Inf Sci (N Y) 2022. [DOI: 10.1016/j.ins.2022.07.123] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022]
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3
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Cao Y, Ramajayam S, Sriraman R, Samidurai R. Leakage delay on stabilization of finite-time complex-valued BAM neural network: Decomposition approach. Neurocomputing 2021. [DOI: 10.1016/j.neucom.2021.08.056] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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4
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Li L, Chen W, Wu X. Global Exponential Stability and Synchronization for Novel Complex-Valued Neural Networks With Proportional Delays and Inhibitory Factors. IEEE TRANSACTIONS ON CYBERNETICS 2021; 51:2142-2152. [PMID: 31647457 DOI: 10.1109/tcyb.2019.2946076] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
In this article, complex-valued neural networks (CVNNs) with proportional delays and inhibitory factors are proposed. First, the global exponential stability of the model addressed is investigated by employing the Halanay inequality technique and the matrix measure method. Some criteria are derived to guarantee the global exponential stability of CVNNs with proportional delays and inhibitory factors. The obtained criteria are applicable not only to systems with proportional delays but also to systems with arbitrary delays. Here, the Lyapunov functions are not constructed. Compared with the Lyapunov method, the matrix measure method makes the obtained criteria more concise, and the Halanay inequality makes the analytical procedure more compact. Furthermore, the global exponential synchronization of two neural-network models with proportional delays and inhibitory factors is also studied. By designing a feedback controller and giving some limitation conditions, the drive system and the response system realize global exponential synchronization. Finally, numerical simulation examples are provided to validate the effectiveness of the theoretical results obtained.
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5
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Finite-time synchronization of complex-valued neural networks with finite-time distributed delays. Neurocomputing 2020. [DOI: 10.1016/j.neucom.2019.01.114] [Citation(s) in RCA: 17] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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6
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Li H, Fang JA, Li X, Rutkowski L, Huang T. Event-triggered impulsive synchronization of discrete-time coupled neural networks with stochastic perturbations and multiple delays. Neural Netw 2020; 132:447-460. [PMID: 33032088 DOI: 10.1016/j.neunet.2020.09.012] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/21/2020] [Revised: 08/06/2020] [Accepted: 09/14/2020] [Indexed: 01/20/2023]
Abstract
This paper deals with the synchronization for discrete-time coupled neural networks (DTCNNs), in which stochastic perturbations and multiple delays are simultaneously involved. The multiple delays mean that both discrete time-varying delays and distributed delays are included. Time-triggered impulsive control (TTIC) is proposed to investigate the synchronization issue of the DTCNNs based on the recently proposed impulsive control scheme for continuous neural networks with single time delays. Furthermore, a novel event-triggered impulsive control (ETIC) is designed to further reduce the communication bandwidth. By using linear matrix inequality (LMI) technique and constructing appropriate Lyapunov functions, some sufficient criteria guaranteeing the synchronization of the DTCNNs are obtained. Finally, We propose a simulation example to illustrate the validity and feasibility of the theoretical results obtained.
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Affiliation(s)
- Huiyuan Li
- College of Information Science and Technology, Donghua University, Shanghai 201620, PR China.
| | - Jian-An Fang
- College of Information Science and Technology, Donghua University, Shanghai 201620, PR China.
| | - Xiaofan Li
- School of Electrical Engineering, Yancheng Institute of Technology, Yancheng 224051, PR China; Key Laboratory of Advanced Perception and Intelligent Control of High-end Equipment of Ministry of Education, Anhui Polytechnic University, Wuhu 241000, PR China.
| | - Leszek Rutkowski
- Institute of Computational Intelligence, Czestochowa University of Technology, 42-200 Czestochowa, Poland; Information Technology Institute, University of Social Sciences, 90-113, ódź, Poland.
| | - Tingwen Huang
- Science Program, Texas A&M University at Qatar, 23874, Doha, Qatar.
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7
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Xu X, Xu Q, Yang J, Xue H, Xu Y. Further research on exponential stability for quaternion-valued neural networks with mixed delays. Neurocomputing 2020. [DOI: 10.1016/j.neucom.2020.03.004] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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8
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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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9
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Li L, Chen W. Exponential stability analysis of quaternion-valued neural networks with proportional delays and linear threshold neurons: Continuous-time and discrete-time cases. Neurocomputing 2020. [DOI: 10.1016/j.neucom.2019.09.051] [Citation(s) in RCA: 17] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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10
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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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11
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Stepanov-Like Pseudo Almost Periodic Solution of Quaternion-Valued for Fuzzy Recurrent Neural Networks with Mixed Delays. Neural Process Lett 2020. [DOI: 10.1007/s11063-020-10193-z] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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12
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Liu J, Jian J. Global dissipativity of a class of quaternion-valued BAM neural networks with time delay. Neurocomputing 2019. [DOI: 10.1016/j.neucom.2019.03.026] [Citation(s) in RCA: 17] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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13
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Stability analysis of fractional Quaternion-Valued Leaky Integrator Echo State Neural Networks with multiple time-varying delays. Neurocomputing 2019. [DOI: 10.1016/j.neucom.2018.11.021] [Citation(s) in RCA: 25] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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14
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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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15
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Liu Y, Qin Y, Huang J, Huang T, Yang X. Finite-Time Synchronization of Complex-Valued Neural Networks with Multiple Time-Varying Delays and Infinite Distributed Delays. Neural Process Lett 2018. [DOI: 10.1007/s11063-018-9958-6] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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16
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Wan P, Jian J. $$\alpha $$
α
-Exponential Stability of Impulsive Fractional-Order Complex-Valued Neural Networks with Time Delays. Neural Process Lett 2018. [DOI: 10.1007/s11063-018-9938-x] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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17
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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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18
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19
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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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20
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Zhang W, Cao J, Chen D, Alsaadi FE. Synchronization in Fractional-Order Complex-Valued Delayed Neural Networks. ENTROPY 2018; 20:e20010054. [PMID: 33265140 PMCID: PMC7512252 DOI: 10.3390/e20010054] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/13/2017] [Revised: 01/07/2018] [Accepted: 01/08/2018] [Indexed: 11/16/2022]
Abstract
This paper discusses the synchronization of fractional order complex valued neural networks (FOCVNN) at the presence of time delay. Synchronization criterions are achieved through the employment of a linear feedback control and comparison theorem of fractional order linear systems with delay. Feasibility and effectiveness of the proposed system are validated through numerical simulations.
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Affiliation(s)
- Weiwei Zhang
- School of Mathematics and Computational Science, Anqing Normal University, Anqing 246011, China
- Correspondence: ; Tel.: +86-152-5566-0785
| | - Jinde Cao
- School of Mathematics, Southeast University, Nanjing 210096, China
- Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
| | - Dingyuan Chen
- School of Mathematics and Computational Science, Anqing Normal University, Anqing 246011, China
| | - Fuad E. Alsaadi
- Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia
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21
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Tang Q, Jian J. Matrix measure based exponential stabilization for complex-valued inertial neural networks with time-varying delays using impulsive control. Neurocomputing 2018. [DOI: 10.1016/j.neucom.2017.08.009] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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22
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New results for exponential stability of complex-valued memristive neural networks with variable delays. Neurocomputing 2018. [DOI: 10.1016/j.neucom.2017.08.066] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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23
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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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24
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Song Q, Shu H, Zhao Z, Liu Y, Alsaadi FE. Lagrange stability analysis for complex-valued neural networks with leakage delay and mixed time-varying delays. Neurocomputing 2017. [DOI: 10.1016/j.neucom.2017.03.015] [Citation(s) in RCA: 53] [Impact Index Per Article: 7.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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25
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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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26
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Gong W, Liang J, Kan X, Wang L, Dobaie AM. Robust state estimation for stochastic complex-valued neural networks with sampled-data. Neural Comput Appl 2017. [DOI: 10.1007/s00521-017-3030-8] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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27
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Jian J, Wan P. Lagrange α-exponential stability and α-exponential convergence for fractional-order complex-valued neural networks. Neural Netw 2017; 91:1-10. [PMID: 28458015 DOI: 10.1016/j.neunet.2017.03.011] [Citation(s) in RCA: 35] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/02/2016] [Revised: 02/15/2017] [Accepted: 03/27/2017] [Indexed: 11/28/2022]
Abstract
This paper deals with the problem on Lagrange α-exponential stability and α-exponential convergence for a class of fractional-order complex-valued neural networks. To this end, some new fractional-order differential inequalities are established, which improve and generalize previously known criteria. By using the new inequalities and coupling with the Lyapunov method, some effective criteria are derived to guarantee Lagrange α-exponential stability and α-exponential convergence of the addressed network. Moreover, the framework of the α-exponential convergence ball is also given, where the convergence rate is related to the parameters and the order of differential of the system. These results here, which the existence and uniqueness of the equilibrium points need not to be considered, generalize and improve the earlier publications and can be applied to monostable and multistable fractional-order complex-valued neural networks. Finally, one example with numerical simulations is given to show the effectiveness of the obtained results.
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Affiliation(s)
- Jigui Jian
- College of Science, China Three Gorges University, Yichang, Hubei, 443002, China.
| | - Peng Wan
- College of Science, China Three Gorges University, Yichang, Hubei, 443002, China.
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28
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29
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Ding X, Cao J, Zhao X, Alsaadi FE. Finite-time Stability of Fractional-order Complex-valued Neural Networks with Time Delays. Neural Process Lett 2017. [DOI: 10.1007/s11063-017-9604-8] [Citation(s) in RCA: 33] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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30
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Wang X, Che M, Wei Y. Complex-valued neural networks for the Takagi vector of complex symmetric matrices. Neurocomputing 2017. [DOI: 10.1016/j.neucom.2016.10.034] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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31
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Finite-Time Synchronization of Complex-Valued Neural Networks with Mixed Delays and Uncertain Perturbations. Neural Process Lett 2017. [DOI: 10.1007/s11063-017-9590-x] [Citation(s) in RCA: 72] [Impact Index Per Article: 10.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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32
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Liu D, Zhu S, Chang W. Input-to-state stability of memristor-based complex-valued neural networks with time delays. Neurocomputing 2017. [DOI: 10.1016/j.neucom.2016.09.075] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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33
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Liang J, Gong W, Huang T. Multistability of complex-valued neural networks with discontinuous activation functions. Neural Netw 2016; 84:125-142. [PMID: 27718391 DOI: 10.1016/j.neunet.2016.08.008] [Citation(s) in RCA: 61] [Impact Index Per Article: 7.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/30/2016] [Revised: 06/21/2016] [Accepted: 08/23/2016] [Indexed: 11/29/2022]
Abstract
In this paper, based on the geometrical properties of the discontinuous activation functions and the Brouwer's fixed point theory, the multistability issue is tackled for the complex-valued neural networks with discontinuous activation functions and time-varying delays. To address the network with discontinuous functions, Filippov solution of the system is defined. Through rigorous analysis, several sufficient criteria are obtained to assure the existence of 25n equilibrium points. Among them, 9n points are locally stable and 16n-9n equilibrium points are unstable. Furthermore, to enlarge the attraction basins of the 9n equilibrium points, some mild conditions are imposed. Finally, one numerical example is provided to illustrate the effectiveness of the obtained results.
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Affiliation(s)
- Jinling Liang
- Department of Mathematics, Southeast University, Nanjing 210096, China.
| | - Weiqiang Gong
- Department of Mathematics, Southeast University, Nanjing 210096, China.
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34
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Xie D, Jiang Y. Global exponential stability of periodic solution for delayed complex-valued neural networks with impulses. Neurocomputing 2016. [DOI: 10.1016/j.neucom.2016.04.054] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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35
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Synchronization of fractional-order complex-valued neural networks with time delay. Neural Netw 2016; 81:16-28. [DOI: 10.1016/j.neunet.2016.05.003] [Citation(s) in RCA: 191] [Impact Index Per Article: 23.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/25/2015] [Revised: 03/20/2016] [Accepted: 05/09/2016] [Indexed: 11/23/2022]
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36
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Global exponential stability of impulsive complex-valued neural networks with both asynchronous time-varying and continuously distributed delays. Neural Netw 2016; 81:1-10. [DOI: 10.1016/j.neunet.2016.04.012] [Citation(s) in RCA: 140] [Impact Index Per Article: 17.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/03/2016] [Revised: 04/25/2016] [Accepted: 04/29/2016] [Indexed: 11/22/2022]
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37
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Global exponential stability of complex-valued neural networks with both time-varying delays and impulsive effects. Neural Netw 2016; 79:108-16. [DOI: 10.1016/j.neunet.2016.03.007] [Citation(s) in RCA: 164] [Impact Index Per Article: 20.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/15/2015] [Revised: 01/30/2016] [Accepted: 03/17/2016] [Indexed: 11/19/2022]
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38
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Analysis of globalO(t−α)stability and global asymptotical periodicity for a class of fractional-order complex-valued neural networks with time varying delays. Neural Netw 2016; 77:51-69. [DOI: 10.1016/j.neunet.2016.01.007] [Citation(s) in RCA: 60] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/01/2015] [Revised: 12/08/2015] [Accepted: 01/13/2016] [Indexed: 11/15/2022]
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39
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Gong W, Liang J, Zhang C. Multistability of complex-valued neural networks with distributed delays. Neural Comput Appl 2016. [DOI: 10.1007/s00521-016-2305-9] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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40
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Liu X, Chen T. Global Exponential Stability for Complex-Valued Recurrent Neural Networks With Asynchronous Time Delays. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2016; 27:593-606. [PMID: 25872218 DOI: 10.1109/tnnls.2015.2415496] [Citation(s) in RCA: 51] [Impact Index Per Article: 6.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
In this paper, we investigate the global exponential stability for complex-valued recurrent neural networks with asynchronous time delays by decomposing complex-valued networks to real and imaginary parts and construct an equivalent real-valued system. The network model is described by a continuous-time equation. There are two main differences of this paper with previous works: 1) time delays can be asynchronous, i.e., delays between different nodes are different, which make our model more general and 2) we prove the exponential convergence directly, while the existence and uniqueness of the equilibrium point is just a direct consequence of the exponential convergence. Using three generalized norms, we present some sufficient conditions for the uniqueness and global exponential stability of the equilibrium point for delayed complex-valued neural networks. These conditions in our results are less restrictive because of our consideration of the excitatory and inhibitory effects between neurons; so previous works of other researchers can be extended. Finally, some numerical simulations are given to demonstrate the correctness of our obtained results.
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41
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Song Q, Zhao Z. Stability criterion of complex-valued neural networks with both leakage delay and time-varying delays on time scales. Neurocomputing 2016. [DOI: 10.1016/j.neucom.2015.06.032] [Citation(s) in RCA: 66] [Impact Index Per Article: 8.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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42
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43
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44
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Chen X, Song Q, Zhao Z, Liu Y. Global μ -stability analysis of discrete-time complex-valued neural networks with leakage delay and mixed delays. Neurocomputing 2016. [DOI: 10.1016/j.neucom.2015.10.120] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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45
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Li Y, Liao X, Li H. Global attracting sets of non-autonomous and complex-valued neural networks with time-varying delays. Neurocomputing 2016. [DOI: 10.1016/j.neucom.2015.08.056] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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46
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Song Q, Zhao Z, Liu Y. Impulsive effects on stability of discrete-time complex-valued neural networks with both discrete and distributed time-varying delays. Neurocomputing 2015. [DOI: 10.1016/j.neucom.2015.05.020] [Citation(s) in RCA: 55] [Impact Index Per Article: 6.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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47
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Gong W, Liang J, Cao J. Global μ-stability of complex-valued delayed neural networks with leakage delay. Neurocomputing 2015. [DOI: 10.1016/j.neucom.2015.06.006] [Citation(s) in RCA: 31] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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48
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Matrix measure method for global exponential stability of complex-valued recurrent neural networks with time-varying delays. Neural Netw 2015; 70:81-9. [DOI: 10.1016/j.neunet.2015.07.003] [Citation(s) in RCA: 90] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/09/2015] [Revised: 05/19/2015] [Accepted: 07/05/2015] [Indexed: 11/21/2022]
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49
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Gong W, Liang J, Zhang C, Cao J. Nonlinear Measure Approach for the Stability Analysis of Complex-Valued Neural Networks. Neural Process Lett 2015. [DOI: 10.1007/s11063-015-9475-9] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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50
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