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Zhou Y, Zhang H, Zeng Z. Quasisynchronization of Memristive Neural Networks With Communication Delays via Event-Triggered Impulsive Control. IEEE TRANSACTIONS ON CYBERNETICS 2022; 52:7682-7693. [PMID: 33296323 DOI: 10.1109/tcyb.2020.3035358] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
This article considers the quasisynchronization of memristive neural networks (MNNs) with communication delays via event-triggered impulsive control (ETIC). In view of the limited communication and bandwidth, we adopt a novel switching event-triggered mechanism (ETM) that not only decreases the times of controller update and the amount of data sent out but also eliminates the Zeno behavior. By using an appropriate Lyapunov function, several algebraic conditions are given for quasisynchronization of MNNs with communication delays. More important, there is no restriction on the derivation of the Lyapunov function, even if it is an increasing function over a period of time. Then, we further propose a switching ETM depending on communication delays and aperiodic sampling, which is more economical and practical and can directly avoid Zeno behavior. Finally, two simulations are presented to validate the effectiveness of the proposed results.
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2
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Liu W, Yang X, Rakkiyappan R, Li X. Dynamic analysis of delayed neural networks: Event-triggered impulsive Halanay inequality approach. Neurocomputing 2022. [DOI: 10.1016/j.neucom.2022.04.116] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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3
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Zhang H, Li L, Li X. Exponential synchronization of coupled neural networks under stochastic deception attacks. Neural Netw 2021; 145:189-198. [PMID: 34763245 DOI: 10.1016/j.neunet.2021.10.015] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/04/2021] [Revised: 09/16/2021] [Accepted: 10/18/2021] [Indexed: 10/20/2022]
Abstract
In this paper, the issue of synchronization is investigated for coupled neural networks subject to stochastic deception attacks. Firstly, a general differential inequality with delayed impulses is given. Then, the established differential inequality is further extended to the case of delayed stochastic impulses, in which both the impulsive instants and impulsive intensity are stochastic. Secondly, by modeling the stochastic discrete-time deception attacks as stochastic impulses, synchronization criteria of the coupled neural networks under the corresponding attacks are given. Finally, two numerical examples are provided to demonstrate the correctness of the theoretical results.
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Affiliation(s)
- Huihui Zhang
- School of Mathematics, Hefei University of Technology, Hefei, 230009, China.
| | - Lulu Li
- School of Mathematics, Hefei University of Technology, Hefei, 230009, China.
| | - Xiaodi Li
- School of Mathematics and Statistics, Shandong Normal University, Ji'nan 250014, China.
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4
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Li L, Sun Y, Wang M, Huang W. Synchronization of Coupled Memristor Neural Networks with Time Delay: Positive Effects of Stochastic Delayed Impulses. Neural Process Lett 2021. [DOI: 10.1007/s11063-021-10600-z] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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5
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Zhang X, Li C, He Z. Cluster synchronization of delayed coupled neural networks: Delay-dependent distributed impulsive control. Neural Netw 2021; 142:34-43. [PMID: 33965886 DOI: 10.1016/j.neunet.2021.04.026] [Citation(s) in RCA: 15] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/20/2020] [Revised: 03/09/2021] [Accepted: 04/20/2021] [Indexed: 11/25/2022]
Abstract
This paper investigates the issue of cluster synchronization (CS) for the coupled neural networks (CNNs) with time-varying delays via the delay-dependent distributed impulsive control. A new Halanay-like inequality, where delayed impulses are taken into consideration, is proposed. Based on the Lyapunov theory and the new differential inequality, sufficient conditions of CS for delayed CNNs with fixed and switching coupling topology are obtained, respectively. Moreover, delay-dependent distributed impulsive controllers with fixed or switching topology are designed thereby. Finally, we present a numerical example of CNNs with fixed or switching coupling to verify the effectiveness of our results, respectively.
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Affiliation(s)
- Xiaoyu Zhang
- Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, College of Electronic and Information Engineering, Southwest University, Chongqing, 400715, PR China
| | - Chuandong Li
- Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, College of Electronic and Information Engineering, Southwest University, Chongqing, 400715, PR China.
| | - Zhilong He
- Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, College of Electronic and Information Engineering, Southwest University, Chongqing, 400715, PR China
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6
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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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7
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Adaptive Synchronization of Complex Dynamical Networks via Distributed Pinning Impulsive Control. Neural Process Lett 2020. [DOI: 10.1007/s11063-020-10373-x] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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8
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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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9
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Li X, Wang N, Lou J, Lu J. Global μ-synchronization of impulsive pantograph neural networks. Neural Netw 2020; 131:78-92. [PMID: 32763762 DOI: 10.1016/j.neunet.2020.07.004] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/06/2020] [Revised: 06/04/2020] [Accepted: 07/06/2020] [Indexed: 11/16/2022]
Abstract
This paper investigates the problem of global μ-synchronization of impulsive pantograph neural networks. In this paper, new concept of ν-asymptotic periodic impulsive interval Tasyν is proposed for pantograph networks. By employing the Lyapunov method combined with the mathematical analysis approach for impulsive systems, some useful criteria are derived to guarantee the global μ-synchronization of coupled pantograph neural networks when the asymptotic logarithmic periodic impulsive interval Tasyln<∞ and Tasyln=∞, respectively. Especially when Tasyln=∞, as long as the networks are unstable, impulsive control cannot achieve synchronization regardless of the size of the impulse gain. Numerical simulations are exploited to illustrate our theoretical results.
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Affiliation(s)
- Xuechen Li
- School of Science, Xuchang University, Xuchang 461000, China
| | - Nan Wang
- School of Science, Xuchang University, Xuchang 461000, China
| | - Jungang Lou
- Zhejiang Province Key Laboratory of Smart Management & Application of Modern Agricultural Resources, Huzhou University, China.
| | - Jianquan Lu
- School of Mathematics, Southeast University, Nanjing 210096, China; School of Automation and Electrical Engineering, Linyi University, Linyi 276005, Shandong, China.
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10
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Synchronization of coupled neural networks under mixed impulsive effects: A novel delay inequality approach. Neural Netw 2020; 127:38-46. [DOI: 10.1016/j.neunet.2020.04.002] [Citation(s) in RCA: 33] [Impact Index Per Article: 8.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/04/2019] [Revised: 03/25/2020] [Accepted: 04/01/2020] [Indexed: 11/19/2022]
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11
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Xu Z, Li X, Duan P. Synchronization of complex networks with time-varying delay of unknown bound via delayed impulsive control. Neural Netw 2020; 125:224-232. [DOI: 10.1016/j.neunet.2020.02.003] [Citation(s) in RCA: 27] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/21/2019] [Revised: 01/03/2020] [Accepted: 02/10/2020] [Indexed: 11/15/2022]
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12
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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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13
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Exponential synchronization of time-varying delayed complex-valued neural networks under hybrid impulsive controllers. Neural Netw 2019; 114:157-163. [DOI: 10.1016/j.neunet.2019.02.006] [Citation(s) in RCA: 37] [Impact Index Per Article: 7.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/02/2018] [Revised: 01/03/2019] [Accepted: 02/22/2019] [Indexed: 12/14/2022]
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14
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Hu B, Guan ZH, Chen G, Lewis FL. Multistability of Delayed Hybrid Impulsive Neural Networks With Application to Associative Memories. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2019; 30:1537-1551. [PMID: 30296243 DOI: 10.1109/tnnls.2018.2870553] [Citation(s) in RCA: 17] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
The important topic of multistability of continuous-and discrete-time neural network (NN) models has been investigated rather extensively. Concerning the design of associative memories, multistability of delayed hybrid NNs is studied in this paper with an emphasis on the impulse effects. Arising from the spiking phenomenon in biological networks, impulsive NNs provide an efficient model for synaptic interconnections among neurons. Using state-space decomposition, the coexistence of multiple equilibria of hybrid impulsive NNs is analyzed. Multistability criteria are then established regrading delayed hybrid impulsive neurodynamics, for which both the impulse effects on the convergence rate and the basins of attraction of the equilibria are discussed. Illustrative examples are given to verify the theoretical results and demonstrate an application to the design of associative memories. It is shown by an experimental example that delayed hybrid impulsive NNs have the advantages of high storage capacity and high fault tolerance when used for associative memories.
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15
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Yang Z, Zhou W, Huang T. Input-to-state stability of delayed reaction-diffusion neural networks with impulsive effects. Neurocomputing 2019. [DOI: 10.1016/j.neucom.2018.12.019] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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16
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Zhou Y, Zeng Z. Event-triggered impulsive control on quasi-synchronization of memristive neural networks with time-varying delays. Neural Netw 2019; 110:55-65. [DOI: 10.1016/j.neunet.2018.09.014] [Citation(s) in RCA: 52] [Impact Index Per Article: 10.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/12/2018] [Revised: 09/17/2018] [Accepted: 09/28/2018] [Indexed: 11/28/2022]
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17
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Time-delay-induced instabilities and Hopf bifurcation analysis in 2-neuron network model with reaction–diffusion term. Neurocomputing 2018. [DOI: 10.1016/j.neucom.2018.06.008] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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18
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Stability Analysis of Cohen–Grossberg Neural Networks with Random Impulses. MATHEMATICS 2018. [DOI: 10.3390/math6090144] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
The Cohen and Grossberg neural networks model is studied in the case when the neurons are subject to a certain impulsive state displacement at random exponentially-distributed moments. These types of impulses significantly change the behavior of the solutions from a deterministic one to a stochastic process. We examine the stability of the equilibrium of the model. Some sufficient conditions for the mean-square exponential stability and mean exponential stability of the equilibrium of general neural networks are obtained in the case of the time-varying potential (or voltage) of the cells, with time-dependent amplification functions and behaved functions, as well as time-varying strengths of connectivity between cells and variable external bias or input from outside the network to the units. These sufficient conditions are explicitly expressed in terms of the parameters of the system, and hence, they are easily verifiable. The theory relies on a modification of the direct Lyapunov method. We illustrate our theory on a particular nonlinear neural network.
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19
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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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20
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Wang Y, Lu J, Lou J, Ding C, Alsaadi FE, Hayat T. Synchronization of Heterogeneous Partially Coupled Networks with Heterogeneous Impulses. Neural Process Lett 2017. [DOI: 10.1007/s11063-017-9735-y] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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21
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Li H, Li C, Huang T. Periodicity and stability for variable-time impulsive neural networks. Neural Netw 2017; 94:24-33. [DOI: 10.1016/j.neunet.2017.06.006] [Citation(s) in RCA: 30] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/01/2017] [Revised: 04/27/2017] [Accepted: 06/09/2017] [Indexed: 10/19/2022]
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22
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Cui Y, Liu Y, Zhang W, Hayat T, Alsaedi A. Sampled-data state estimation for a class of delayed complex networks via intermittent transmission. Neurocomputing 2017. [DOI: 10.1016/j.neucom.2017.04.031] [Citation(s) in RCA: 7] [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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23
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Wang L, Song Q, Liu Y, Zhao Z, Alsaadi FE. Global asymptotic stability of impulsive fractional-order complex-valued neural networks with time delay. Neurocomputing 2017. [DOI: 10.1016/j.neucom.2017.02.086] [Citation(s) in RCA: 28] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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24
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Li J, Zhou W, Yang Z. State estimation and input-to-state stability of impulsive stochastic BAM neural networks with mixed delays. Neurocomputing 2017. [DOI: 10.1016/j.neucom.2016.08.101] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/01/2022]
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25
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Duan S, Wang H, Wang L, Huang T, Li C. Impulsive Effects and Stability Analysis on Memristive Neural Networks With Variable Delays. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2017; 28:476-481. [PMID: 26742146 DOI: 10.1109/tnnls.2015.2497319] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
In this brief, hybrid impulsive and adaptive feedback controllers are simultaneously exerted on a general delayed memristive neural network (MNN) model to formulate a novel impulsive controlled MNN (IMNN) model with variable delays. By means of Lyapunov-Razumikhin technique and other analytical ways, several new stability criteria of the proposed IMNN model are obtained. In addition, by choosing appropriate impulses and external inputs, the convergence speed of IMNN can be increased, which implies that its dynamic behaviors will be optimized. Finally, the effectiveness of the obtained results is illustrated by one numerical example.
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26
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Novel Existence and Stability Criteria of Periodic Solutions for Impulsive Delayed Neural Networks Via Coefficient Integral Averages. Neurocomputing 2016. [DOI: 10.1016/j.neucom.2016.08.027] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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27
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Global exponential stability of memristive neural networks with impulse time window and time-varying delays. Neurocomputing 2016. [DOI: 10.1016/j.neucom.2015.07.040] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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28
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Zhou Y, Li C, Huang T, Wang X. Impulsive stabilization and synchronization of Hopfield-type neural networks with impulse time window. Neural Comput Appl 2015. [DOI: 10.1007/s00521-015-2105-7] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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29
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Wang H, Duan S, Li C, Wang L, Huang T. Exponential stability analysis of delayed memristor-based recurrent neural networks with impulse effects. Neural Comput Appl 2015. [DOI: 10.1007/s00521-015-2094-6] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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30
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Jiang Y, Li C. Exponential stability of memristor-based synchronous switching neural networks with time delays. INT J BIOMATH 2015. [DOI: 10.1142/s1793524516500169] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
In this paper, we study the existence, uniqueness and stability of memristor-based synchronous switching neural networks with time delays. Several criteria of exponential stability are given by introducing multiple Lyapunov functions. In comparison with the existing publications on simplice memristive neural networks or switching neural networks, we consider a system with a series of switchings, these switchings are assumed to be synchronous with memristive switching mechanism. Moreover, the proposed stability conditions are straightforward and convenient and can reflect the impact of time delay on the stability. Two examples are also presented to illustrate the effectiveness of the theoretical results.
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Affiliation(s)
- Yinlu Jiang
- College of Electronic and Information Engineering, Southwest University, Chongqing 400715, P. R. China
| | - Chuandong Li
- College of Electronic and Information Engineering, Southwest University, Chongqing 400715, P. R. China
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31
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Zhang W, Tang Y, Wong WK, Miao Q. Stochastic stability of delayed neural networks with local impulsive effects. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2015; 26:2336-2345. [PMID: 25546865 DOI: 10.1109/tnnls.2014.2380451] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
In this paper, the stability problem is studied for a class of stochastic neural networks (NNs) with local impulsive effects. The impulsive effects considered can be not only nonidentical in different dimensions of the system state but also various at distinct impulsive instants. Hence, the impulses here can encompass several typical impulses in NNs. The aim of this paper is to derive stability criteria such that stochastic NNs with local impulsive effects are exponentially stable in mean square. By means of the mathematical induction method, several easy-to-check conditions are obtained to ensure the mean square stability of NNs. Three examples are given to show the effectiveness of the proposed stability criterion.
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32
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Kumar RS, Sugumaran G, Raja R, Zhu Q, Raja UK. New stability criterion of neural networks with leakage delays and impulses: a piecewise delay method. Cogn Neurodyn 2015; 10:85-98. [PMID: 26834863 DOI: 10.1007/s11571-015-9356-y] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/26/2015] [Revised: 09/06/2015] [Accepted: 09/15/2015] [Indexed: 11/24/2022] Open
Abstract
This paper analyzes the global asymptotic stability of a class of neural networks with time delay in the leakage term and time-varying delays under impulsive perturbations. Here the time-varying delays are assumed to be piecewise. In this method, the interval of the variation is divided into two subintervals by its central point. By developing a new Lyapunov-Krasovskii functional and checking its variation in between the two subintervals, respectively, and then we present some sufficient conditions to guarantee the global asymptotic stability of the equilibrium point for the considered neural network. The proposed results which do not require the boundedness, differentiability and monotonicity of the activation functions, can be easily verified via the linear matrix inequality (LMI) control toolbox in MATLAB. Finally, a numerical example and its simulation are given to show the conditions obtained are new and less conservative than some existing ones in the literature.
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Affiliation(s)
- R Suresh Kumar
- Department of Electrical and Electronic Engineering, Anna University Regional Centre, Coimbatore, 641 047 India
| | - G Sugumaran
- Department of Electrical and Electronic Engineering, Sri Krishna College of Engineering and Technology, Coimbatore, 641 008 India
| | - R Raja
- Ramanujan Centre for Higher Mathematics, Alagappa University, Karaikudi, 630 004 India
| | - Quanxin Zhu
- School of Mathematical Sciences and Institute of Finance and Statistics, Nanjing Normal University, Nanjing, 210 023 China
| | - U Karthik Raja
- Department of Mathematics, K.S.R College of Arts and Science, Thiruchengodu, 637 215 India
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34
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Qi J, Li C, Huang T. Stability of delayed memristive neural networks with time-varying impulses. Cogn Neurodyn 2014; 8:429-36. [PMID: 25206936 DOI: 10.1007/s11571-014-9286-0] [Citation(s) in RCA: 35] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/06/2013] [Revised: 12/18/2013] [Accepted: 03/13/2014] [Indexed: 10/25/2022] Open
Abstract
This paper addresses the stability problem on the memristive neural networks with time-varying impulses. Based on the memristor theory and neural network theory, the model of the memristor-based neural network is established. Different from the most publications on memristive networks with fixed-time impulse effects, we consider the case of time-varying impulses. Both the destabilizing and stabilizing impulses exist in the model simultaneously. Through controlling the time intervals of the stabilizing and destabilizing impulses, we ensure the effect of the impulses is stabilizing. Several sufficient conditions for the globally exponentially stability of memristive neural networks with time-varying impulses are proposed. The simulation results demonstrate the effectiveness of the theoretical results.
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Affiliation(s)
- Jiangtao Qi
- College of Computer Science, Chongqing University, Chongqing, 400044 China
| | - Chuandong Li
- College of Computer Science, Chongqing University, Chongqing, 400044 China
| | - Tingwen Huang
- Department of Mathematics, Texas A&M University at Qatar, PO Box 23874, Doha, Qatar
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35
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Zhang W, Tang Y, Wu X, Fang JA. Stochastic Stability of Switched Genetic Regulatory Networks With Time-Varying Delays. IEEE Trans Nanobioscience 2014; 13:336-42. [DOI: 10.1109/tnb.2014.2327582] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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36
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Liu B, Lu W, Chen T. Pinning consensus in networks of multiagents via a single impulsive controller. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2013; 24:1141-1149. [PMID: 24808527 DOI: 10.1109/tnnls.2013.2247059] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
In this paper, we discuss pinning consensus in networks of multiagents via impulsive controllers. In particular, we consider the case of using only one impulsive controller. We provide a sufficient condition to pin the network to a prescribed value. It is rigorously proven that in case the underlying graph of the network has spanning trees, the network can reach consensus on the prescribed value when the impulsive controller is imposed on the root with appropriate impulsive strength and impulse intervals. Interestingly, we find that the permissible range of the impulsive strength completely depends on the left eigenvector of the graph Laplacian corresponding to the zero eigenvalue and the pinning node we choose. The impulses can be very sparse, with the impulsive intervals being lower bounded. Examples with numerical simulations are also provided to illustrate the theoretical results.
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37
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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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38
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Zhang W, Tang Y, Fang JA, Zhu W. Exponential cluster synchronization of impulsive delayed genetic oscillators with external disturbances. CHAOS (WOODBURY, N.Y.) 2011; 21:043137. [PMID: 22225374 DOI: 10.1063/1.3671609] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
This paper investigates the problem of the exponential cluster synchronization of coupled impulsive genetic oscillators with external disturbances and communication delay. Based on the Kronecker product, some new cluster synchronization criteria for coupled impulsive genetic oscillators with attenuation level are derived. The derived results are related to the impulsive strength, and the derived results also indicate that the maximal allowable bound of time delay is inversely proportional to the decay rate, the decay rate is proportional to the couple strength, the maximal allowable bound of time delay is proportional to attenuation level, and the attenuation level is inversely proportional to the couple strength. Moreover, the case when the feedback have different self-delay is also investigated. Finally, numerical examples are given to illustrate the effectiveness of the derived results.
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Affiliation(s)
- Wenbing Zhang
- School of Information Science and Technology, Donghua University, Shanghai 201620, China.
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CHEN JUN, CUI BAOTONG, JI YAN. NEW CRITERIA OF ALMOST PERIODIC SOLUTION FOR BAM NEURAL NETWORKS WITH DELAYS AND IMPULSIVE EFFECTS. Int J Neural Syst 2011; 17:395-406. [DOI: 10.1142/s0129065707001238] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
This paper presents some sufficient conditions for the existence and global exponential stability of the almost periodic solution for impulsive bi-directional associative memory neural networks with time-varying delays by using Lyapunov functional and Gronwall-Bellmans inequality technique. Comparing with known literatures, the results of this paper are new and they complement previously known results.
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Affiliation(s)
- JUN CHEN
- College of Communication and Control Engineering, Jiangnan University, 1800 Lihu Rd., Wuxi, Jiangsu 214122, P. R. China
| | - BAOTONG CUI
- College of Communication and Control Engineering, Jiangnan University, 1800 Lihu Rd., Wuxi, Jiangsu 214122, P. R. China
| | - YAN JI
- College of Communication and Control Engineering, Jiangnan University, 1800 Lihu Rd., Wuxi, Jiangsu 214122, P. R. China
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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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Lu J, Ho DWC, Cao J, Kurths J. Exponential Synchronization of Linearly Coupled Neural Networks With Impulsive Disturbances. ACTA ACUST UNITED AC 2011; 22:329-36. [DOI: 10.1109/tnn.2010.2101081] [Citation(s) in RCA: 304] [Impact Index Per Article: 23.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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42
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Asymptotic behavior of equilibriums of a class of impulsive bidirectional associative memory neural networks with time-varying delays. Neural Comput Appl 2011. [DOI: 10.1007/s00521-010-0516-z] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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Allegretto W, Papini D, Forti M. Common Asymptotic Behavior of Solutions and Almost Periodicity for Discontinuous, Delayed, and Impulsive Neural Networks. ACTA ACUST UNITED AC 2010; 21:1110-25. [DOI: 10.1109/tnn.2010.2048759] [Citation(s) in RCA: 64] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
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Cheng Hu, Haijun Jiang, Zhidong Teng. Impulsive Control and Synchronization for Delayed Neural Networks With Reaction–Diffusion Terms. ACTA ACUST UNITED AC 2010; 21:67-81. [DOI: 10.1109/tnn.2009.2034318] [Citation(s) in RCA: 185] [Impact Index Per Article: 13.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Li C, Chen L, Aihara K. Impulsive control of stochastic systems with applications in chaos control, chaos synchronization, and neural networks. CHAOS (WOODBURY, N.Y.) 2008; 18:023132. [PMID: 18601498 DOI: 10.1063/1.2939483] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/26/2023]
Abstract
Real systems are often subject to both noise perturbations and impulsive effects. In this paper, we study the stability and stabilization of systems with both noise perturbations and impulsive effects. In other words, we generalize the impulsive control theory from the deterministic case to the stochastic case. The method is based on extending the comparison method to the stochastic case. The method presented in this paper is general and easy to apply. Theoretical results on both stability in the pth mean and stability with disturbance attenuation are derived. To show the effectiveness of the basic theory, we apply it to the impulsive control and synchronization of chaotic systems with noise perturbations, and to the stability of impulsive stochastic neural networks. Several numerical examples are also presented to verify the theoretical results.
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Affiliation(s)
- Chunguang Li
- Centre for Nonlinear and Complex Systems, School of Electronic Engineering, University of Electronic Science and Technology of China, Chengdu 610054, People's Republic of China
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Lu JG, Hill DJ. Impulsive Synchronization of Chaotic Lur'e Systems by Linear Static Measurement Feedback: An LMI Approach. ACTA ACUST UNITED AC 2007. [DOI: 10.1109/tcsii.2007.898468] [Citation(s) in RCA: 77] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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