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Sheng Y, Zeng Z, Huang T. Global Stability of Bidirectional Associative Memory Neural Networks With Multiple Time-Varying Delays. IEEE TRANSACTIONS ON CYBERNETICS 2022; 52:4095-4104. [PMID: 32784149 DOI: 10.1109/tcyb.2020.3011581] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
This article investigates the global stability of bidirectional associative memory neural networks with discrete and distributed time-varying delays (DBAMNNs). By employing the comparison strategy and inequality techniques, global asymptotic stability (GAS) and global exponential stability (GES) of the underlying DBAMNNs are of concern in terms of p -norm ( p ≥ 2 ). Meanwhile, GES of the addressed DBAMNNs is also analyzed in terms of 1-norm. When distributed time delay is neglected, the GES of the corresponding bidirectional associative memory neural networks is presented as an M -matrix, which includes certain existing outcomes as special cases. Two examples are finally provided to substantiate the validity of theories.
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2
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Cui Q, Li L, Cao J. Stability of inertial delayed neural networks with stochastic delayed impulses via matrix measure method. Neurocomputing 2022. [DOI: 10.1016/j.neucom.2021.10.113] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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3
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Sun Y, Li L, Liu X. Exponential synchronization of neural networks with time-varying delays and stochastic impulses. Neural Netw 2020; 132:342-352. [DOI: 10.1016/j.neunet.2020.09.014] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/04/2020] [Revised: 08/05/2020] [Accepted: 09/14/2020] [Indexed: 12/16/2022]
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4
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Mu G, Li L, Li X. Quasi-bipartite synchronization of signed delayed neural networks under impulsive effects. Neural Netw 2020; 129:31-42. [DOI: 10.1016/j.neunet.2020.05.012] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/04/2020] [Revised: 04/19/2020] [Accepted: 05/11/2020] [Indexed: 10/24/2022]
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5
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Li X, Cao J, Ho DWC. Impulsive Control of Nonlinear Systems With Time-Varying Delay and Applications. IEEE TRANSACTIONS ON CYBERNETICS 2020; 50:2661-2673. [PMID: 30762581 DOI: 10.1109/tcyb.2019.2896340] [Citation(s) in RCA: 26] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
Impulsive control of nonlinear delay systems is studied in this paper, where the time delays addressed may be the constant delay, bounded time-varying delay, or unbounded time-varying delay. Based on the impulsive control theory and some analysis techniques, a new theoretical result for global exponential stability is derived from the impulsive control point of view. The significance of the presented result is that the stability can be achieved via the impulsive control at certain impulse points despite the existence of impulsive perturbations which causes negative effect to the control. That is, the impulsive control provides a super performance to allow the existence of impulsive perturbations. In addition, we apply the theoretical result to the problem of impulsive control of delayed neural networks. Some results for global exponential stability and synchronization control of neural networks with time delays are derived via impulsive control. Three illustrated examples are given to show the effectiveness and distinctiveness of the proposed impulsive control schemes.
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6
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Global Exponential Stability of High-Order Bidirectional Associative Memory (BAM) Neural Networks with Proportional Delays. Neural Process Lett 2020. [DOI: 10.1007/s11063-020-10206-x] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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7
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Synchronization of impulsive coupled complex-valued neural networks with delay: The matrix measure method. Neural Netw 2019; 117:285-294. [DOI: 10.1016/j.neunet.2019.05.024] [Citation(s) in RCA: 38] [Impact Index Per Article: 7.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/23/2018] [Revised: 05/09/2019] [Accepted: 05/24/2019] [Indexed: 11/21/2022]
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8
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Yang W, Yu W, Cao J. Global Exponential Stability of Impulsive Fuzzy High-Order BAM Neural Networks With Continuously Distributed Delays. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2018; 29:3682-3700. [PMID: 28880192 DOI: 10.1109/tnnls.2017.2736581] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
This paper investigates the stability of equilibrium point and periodic solution for impulsive fuzzy high-order bidirectional associative memory neural networks with continuously distributed delays. By applying the inequality analysis technique, -matrix, and Banach contraction mapping principle and constructing some suitable Lyapunov functionals, some sufficient conditions for the uniqueness and global exponential stability of equilibrium point and global exponential stability of periodic solutions are established. In addition, three examples with numerical simulations are presented to demonstrate the feasibility and effectiveness of the theoretical results.
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9
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Xu C, Chen L, Guo T. Anti-periodic oscillations of bidirectional associative memory (BAM) neural networks with leakage delays. JOURNAL OF INEQUALITIES AND APPLICATIONS 2018; 2018:68. [PMID: 29628744 PMCID: PMC5882806 DOI: 10.1186/s13660-018-1658-2] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/05/2017] [Accepted: 03/20/2018] [Indexed: 06/08/2023]
Abstract
In this article, we discuss anti-periodic oscillations of BAM neural networks with leakage delays. A sufficient criterion guaranteeing the existence and exponential stability of the involved model is presented by utilizing mathematic analysis methods and Lyapunov ideas. The theoretical results of this article are novel and are a key supplement to some earlier studies.
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Affiliation(s)
- Changjin Xu
- Guizhou Key Laboratory of Economics System Simulation, Guizhou University of Finance and Economics, Guiyang, P.R. China
| | - Lilin Chen
- School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang, P.R. China
| | - Ting Guo
- School of Mathematics and Statistics, Central South University, Changsha, P.R. China
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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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11
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Liu Y, Zhang C, Kao Y, Hou C. Exponential Stability of Neutral-Type Impulsive Markovian Jump Neural Networks with General Incomplete Transition Rates. Neural Process Lett 2017. [DOI: 10.1007/s11063-017-9650-2] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/01/2022]
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12
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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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13
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Arbi A, Aouiti C, Chérif F, Touati A, Alimi AM. Stability analysis for delayed high-order type of Hopfield neural networks with impulses. Neurocomputing 2015. [DOI: 10.1016/j.neucom.2015.03.021] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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14
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Zheng S. Stability of uncertain impulsive complex-variable chaotic systems with time-varying delays. ISA TRANSACTIONS 2015; 58:20-26. [PMID: 26096956 DOI: 10.1016/j.isatra.2015.05.016] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/06/2014] [Revised: 04/19/2015] [Accepted: 05/15/2015] [Indexed: 06/04/2023]
Abstract
In this paper, the robust exponential stabilization of uncertain impulsive complex-variable chaotic delayed systems is considered with parameters perturbation and delayed impulses. It is assumed that the considered complex-variable chaotic systems have bounded parametric uncertainties together with the state variables on the impulses related to the time-varying delays. Based on the theories of adaptive control and impulsive control, some less conservative and easily verified stability criteria are established for a class of complex-variable chaotic delayed systems with delayed impulses. Some numerical simulations are given to validate the effectiveness of the proposed criteria of impulsive stabilization for uncertain complex-variable chaotic delayed systems.
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Affiliation(s)
- Song Zheng
- School of Mathematics and Statistics, Zhejiang University of Finance & Economics, Hangzhou, Zhejiang 310018, PR China.
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15
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Qi J, Li C, Huang T. Existence and exponential stability of periodic solution of delayed Cohen–Grossberg neural networks via impulsive control. Neural Comput Appl 2015. [DOI: 10.1007/s00521-014-1793-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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16
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Wang F, Sun D, Wu H. Global exponential stability and periodic solutions of high-order bidirectional associative memory (BAM) neural networks with time delays and impulses. Neurocomputing 2015. [DOI: 10.1016/j.neucom.2014.12.014] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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17
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Xu C, Zhang Q. Existence and global exponential stability of anti-periodic solutions for BAM neural networks with inertial term and delay. Neurocomputing 2015. [DOI: 10.1016/j.neucom.2014.11.047] [Citation(s) in RCA: 75] [Impact Index Per Article: 8.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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18
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Wang L, Chen T. Multistability and complete convergence analysis on high-order neural networks with a class of nonsmooth activation functions. Neurocomputing 2015. [DOI: 10.1016/j.neucom.2014.10.075] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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19
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Tan M, Xu S, Li Z. Dynamics of High-order Fuzzy Cellular Neural Networks with Time-varying Delays. INT J COMPUT INT SYS 2015. [DOI: 10.1080/18756891.2015.1017368] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022] Open
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20
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Wei L, Chen WH. Global exponential stability of a class of impulsive neural networks with unstable continuous and discrete dynamics. Neurocomputing 2015. [DOI: 10.1016/j.neucom.2014.06.072] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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21
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Şaylı M, Yılmaz E. Global robust asymptotic stability of variable-time impulsive BAM neural networks. Neural Netw 2014; 60:67-73. [DOI: 10.1016/j.neunet.2014.07.016] [Citation(s) in RCA: 40] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/19/2014] [Accepted: 07/31/2014] [Indexed: 10/24/2022]
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22
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Exponential stability of impulsive discrete-time stochastic BAM neural networks with time-varying delay. Neurocomputing 2014. [DOI: 10.1016/j.neucom.2013.10.010] [Citation(s) in RCA: 34] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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23
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Zhang A, Qiu J, She J. Existence and global exponential stability of periodic solution for high-order discrete-time BAM neural networks. Neural Netw 2014; 50:98-109. [DOI: 10.1016/j.neunet.2013.11.005] [Citation(s) in RCA: 32] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/14/2013] [Revised: 09/28/2013] [Accepted: 11/10/2013] [Indexed: 10/26/2022]
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24
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Wang Y, Cao J. Exponential stability of stochastic higher-order BAM neural networks with reaction–diffusion terms and mixed time-varying delays. Neurocomputing 2013. [DOI: 10.1016/j.neucom.2013.03.040] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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25
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Zhang Y. Stochastic stability of discrete-time Markovian jump delay neural networks with impulses and incomplete information on transition probability. Neural Netw 2013; 46:276-82. [DOI: 10.1016/j.neunet.2013.06.009] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/22/2013] [Revised: 06/24/2013] [Accepted: 06/25/2013] [Indexed: 10/26/2022]
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26
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Raja R, Raja UK, Samidurai R, Leelamani A. Dynamic analysis of discrete-time BAM neural networks with stochastic perturbations and impulses. INT J MACH LEARN CYB 2013. [DOI: 10.1007/s13042-013-0199-8] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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27
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28
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Zhang W, Tang Y, Fang JA, Wu X. Stability of delayed neural networks with time-varying impulses. Neural Netw 2012; 36:59-63. [DOI: 10.1016/j.neunet.2012.08.014] [Citation(s) in RCA: 52] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/17/2012] [Revised: 07/28/2012] [Accepted: 08/26/2012] [Indexed: 10/27/2022]
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29
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Multistability and multiperiodicity of high-order competitive neural networks with a general class of activation functions. Neurocomputing 2012. [DOI: 10.1016/j.neucom.2011.09.032] [Citation(s) in RCA: 47] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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30
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Wu B, Liu Y, Lu J. New results on global exponential stability for impulsive cellular neural networks with any bounded time-varying delays. ACTA ACUST UNITED AC 2012. [DOI: 10.1016/j.mcm.2011.09.009] [Citation(s) in RCA: 50] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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31
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SONG QIANKUN, CAO JINDE. STABILITY ANALYSIS OF IMPULSIVE COHEN-GROSSBERG NEURAL NETWORK WITH UNBOUNDED DISCRETE TIME-VARYING DELAYS. Int J Neural Syst 2011; 17:407-17. [DOI: 10.1142/s012906570700124x] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
In this paper, the impulsive Cohen-Grossberg neural network with unbounded discrete time-varying delays is considered. By using the analysis method and inequality technique, several sufficient conditions are obtained to ensure the global exponential stability of the addressed neural network. These results generalize the existing relevant stability results. Two examples with simulations are given to show the effectiveness of the obtained results.
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Affiliation(s)
- QIANKUN SONG
- Department of Mathematics, Chongqing Jiaotong University, Chongqing 400074, China
| | - JINDE CAO
- Department of Mathematics, Southeast University, Nanjing 210096, China
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32
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JIANG HAIJUN, LIU JING. DYNAMICS ANALYSIS OF IMPULSIVE STOCHASTIC HIGH-ORDER BAM NEURAL NETWORKS WITH MARKOVIAN JUMPING AND MIXED DELAYS. INT J BIOMATH 2011. [DOI: 10.1142/s1793524511001398] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
This paper deals with the problem of asymptotical stability in mean square for a class of impulsive stochastic high-order bi-directional associative memory (BAM) neural networks with mixed delays and Markovian jumping parameters. Based on Lyapunov stability theory, linear matrix inequality and mathematical induction, some sufficient conditions are derived for the asymptotical stability in mean square of the equilibrium point of the neural networks. The results obtained in this paper are new and complement previously known results.
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Affiliation(s)
- HAIJUN JIANG
- College of Mathematics and System Sciences, Xinjiang University, Urumqi, 830046, P. R. China
| | - JING LIU
- College of Mathematics and System Sciences, Xinjiang University, Urumqi, 830046, P. R. China
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33
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Xiaobing Nie, Jinde Cao. Multistability of Second-Order Competitive Neural Networks With Nondecreasing Saturated Activation Functions. ACTA ACUST UNITED AC 2011; 22:1694-708. [DOI: 10.1109/tnn.2011.2164934] [Citation(s) in RCA: 61] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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34
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Wu Q, Zhou J, Xiang L. Impulses-induced exponential stability in recurrent delayed neural networks. Neurocomputing 2011. [DOI: 10.1016/j.neucom.2011.05.001] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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35
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Zhang Y. Robust exponential stability of uncertain impulsive neural networks with time-varying delays and delayed impulses. Neurocomputing 2011. [DOI: 10.1016/j.neucom.2011.05.004] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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36
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37
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Li C, Li C, Liao X, Huang T. Impulsive effects on stability of high-order BAM neural networks with time delays. Neurocomputing 2011. [DOI: 10.1016/j.neucom.2010.12.028] [Citation(s) in RCA: 67] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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38
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Gu H. Mean square exponential stability in high-order stochastic impulsive BAM neural networks with time-varying delays. Neurocomputing 2011. [DOI: 10.1016/j.neucom.2010.09.011] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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39
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Zhang H, Dong M, Wang Y, Sun N. Stochastic stability analysis of neutral-type impulsive neural networks with mixed time-varying delays and Markovian jumping. Neurocomputing 2010. [DOI: 10.1016/j.neucom.2010.04.016] [Citation(s) in RCA: 42] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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40
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Delay-dependent stability analysis for continuous-time BAM neural networks with Markovian jumping parameters. Neural Netw 2010; 23:315-21. [DOI: 10.1016/j.neunet.2009.12.001] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/22/2009] [Revised: 11/26/2009] [Accepted: 12/01/2009] [Indexed: 11/22/2022]
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41
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Ge J, Xu J. Computation of synchronized periodic solution in a BAM network with two delays. IEEE TRANSACTIONS ON NEURAL NETWORKS 2010; 21:439-50. [PMID: 20123571 DOI: 10.1109/tnn.2009.2038911] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Abstract
A bidirectional associative memory (BAM) neural network with four neurons and two discrete delays is considered to represent an analytical method, namely, perturbation-incremental scheme (PIS). The expressions for the periodic solutions derived from Hopf bifurcation are given by using the PIS. The result shows that the PIS has higher accuracy than the center manifold reduction (CMR) with normal form for the values of time delay not far away from the Hopf bifurcation point. In terms of the PIS, the necessary and sufficient conditions of synchronized periodic solution arising from a Hopf bifurcation are obtained and the synchronized periodic solution is expressed in an analytical form. It can be seen that theoretical analysis is in good agreement with numerical simulation. It implies that the provided method is valid and the obtained result is correct. To the best of our knowledge, the paper is the first one to introduce the PIS to study the periodic solution derived from Hopf bifurcation for a 4-D delayed system quantitatively.
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Affiliation(s)
- Juhong Ge
- School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, China
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42
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Karimi HR, Gao H. Notice of Violation of IEEE Publication Principles: New Delay-Dependent Exponential $H_{\infty}$ Synchronization for Uncertain Neural Networks With Mixed Time Delays. ACTA ACUST UNITED AC 2010; 40:173-85. [DOI: 10.1109/tsmcb.2009.2024408] [Citation(s) in RCA: 413] [Impact Index Per Article: 29.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
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43
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Global Exponential Stability for Impulsive BAM Neural Networks with Distributed Delays on Time Scales. Neural Process Lett 2010. [DOI: 10.1007/s11063-009-9127-z] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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44
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Existence and global attractivity of almost periodic solutions for delayed high-ordered neural networks. Neurocomputing 2010. [DOI: 10.1016/j.neucom.2009.10.007] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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45
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Hu L, Liu H, Zhao Y. New stability criteria for BAM neural networks with time-varying delays. Neurocomputing 2009. [DOI: 10.1016/j.neucom.2009.02.016] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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46
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Liu Y, Wang Z, Liu X. On Global Stability of Delayed BAM Stochastic Neural Networks with Markovian Switching. Neural Process Lett 2009. [DOI: 10.1007/s11063-009-9107-3] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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47
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Dong M, Zhang H, Wang Y. Dynamics analysis of impulsive stochastic Cohen–Grossberg neural networks with Markovian jumping and mixed time delays. Neurocomputing 2009. [DOI: 10.1016/j.neucom.2008.12.007] [Citation(s) in RCA: 49] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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48
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49
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Sun J. Stationary oscillation for chaotic shunting inhibitory cellular neural networks with impulses. CHAOS (WOODBURY, N.Y.) 2007; 17:043123. [PMID: 18163787 DOI: 10.1063/1.2816944] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/25/2023]
Abstract
In this paper, we study stationary oscillation for general shunting inhibitory cellular neural networks with impulses which are complex nonlinear neural networks. In a recent paper [Z. J. Gui and W. G. Ge, Chaos 16, 033116 (2006)], the authors claimed that they obtained a criterion of existence, uniqueness, and global exponential stability of periodic solution (i.e., stationary oscillation) for shunting inhibitory cellular neural networks with impulses. We point out in this paper that the main result of their paper is incorrect, and presents a sufficient condition of ensuring existence, uniqueness, and global stability of periodic solution for general shunting inhibitory cellular neural networks with impulses. The result is derived by using a new method which is different from those of previous literature. An illustrative example is given to demonstrate the effectiveness.
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Affiliation(s)
- Jitao Sun
- Department of Mathematics, Tongji University, Shanghai 200092, China.
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