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Wang J, Zhu S, Mu C, Liu X, Wen S. Unified analysis on multistablity of fraction-order multidimensional-valued memristive neural networks. Neural Netw 2024; 179:106498. [PMID: 38986183 DOI: 10.1016/j.neunet.2024.106498] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/05/2024] [Revised: 04/29/2024] [Accepted: 06/26/2024] [Indexed: 07/12/2024]
Abstract
This article provides a unified analysis of the multistability of fraction-order multidimensional-valued memristive neural networks (FOMVMNNs) with unbounded time-varying delays. Firstly, based on the knowledge of fractional differentiation and memristors, a unified model is established. This model is a unified form of real-valued, complex-valued, and quaternion-valued systems. Then, based on a unified method, the number of equilibrium points for FOMVMNNs is discussed. The sufficient conditions for determining the number of equilibrium points have been obtained. By using 1-norm to construct Lyapunov functions, the unified criteria for multistability of FOMVMNNs are obtained, these criteria are less conservative and easier to verify. Moreover, the attraction basins of the stable equilibrium points are estimated. Finally, two numerical simulation examples are provided to verify the correctness of the results.
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Affiliation(s)
- Jiarui Wang
- School of Mathematics, China University of Mining and Technology, Xuzhou, 221116, China.
| | - Song Zhu
- School of Mathematics, China University of Mining and Technology, Xuzhou, 221116, China.
| | - Chaoxu Mu
- School of Electrical and Automation Engineering, Tianjin University, Tianjin, 300072, China.
| | - Xiaoyang Liu
- School of Computer Science and Technology, Jiangsu Normal University, Xuzhou, 221116, China.
| | - Shiping Wen
- Centre for Artificial Intelligence, University of Technology Sydney, Ultimo, NSW 2007, Australia.
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Chen J, Chen B, Zeng Z. Exponential quasi-synchronization of coupled delayed memristive neural networks via intermittent event-triggered control. Neural Netw 2021; 141:98-106. [PMID: 33878659 DOI: 10.1016/j.neunet.2021.01.013] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/05/2020] [Revised: 12/16/2020] [Accepted: 01/14/2021] [Indexed: 10/22/2022]
Abstract
Firstly, an intermittent event-triggered control (IETC), as a combination of intermittent control and event-triggered control, is proposed. Then, the quasi-synchronization problem of coupled memristive neural networks with time-varying delays (CDMNN) is discussed under this IETC. To include more of the existing work, aperiodic intermittent control and event-triggered control with combined measurement errors are adopted in the IETC. Under the IETC, it is shown that Zeno behavior cannot be exhibited for CDMNN. At the same time, two new differential inequalities are established, and some simple and practical criteria for CDMNN quasi-synchronization and synchronization are obtained by using these inequalities. In the obtained results, synchronization is a spatial case of quasi-synchronization, and the activation functions of DMNN do not need to be bounded. Finally, a numerical example and some simulations are provided to test the results in theoretical analysis.
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Affiliation(s)
- Jiejie Chen
- The College of Computer Science and Information Engineering, Hubei Normal University, Huangshi 435002, China; Key Laboratory of Image Processing and Intelligent Control of Education Ministry of China, Wuhan 430074, China.
| | - Boshan Chen
- The College of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China.
| | - Zhigang Zeng
- School of Automation, Huazhong University of Science and Technology, Wuhan 430074, China; Key Laboratory of Image Processing and Intelligent Control of Education Ministry of China, Wuhan 430074, China.
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Rajan R, Gandhi V, Soundharajan P, Joo YH. Almost periodic dynamics of memristive inertial neural networks with mixed delays. Inf Sci (N Y) 2020. [DOI: 10.1016/j.ins.2020.05.055] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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Zhu S, Liu D, Yang C, Fu J. Synchronization of Memristive Complex-Valued Neural Networks With Time Delays via Pinning Control Method. IEEE TRANSACTIONS ON CYBERNETICS 2020; 50:3806-3815. [PMID: 31689227 DOI: 10.1109/tcyb.2019.2946703] [Citation(s) in RCA: 31] [Impact Index Per Article: 7.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
This article concentrates on the synchronization problem of memristive complex-valued neural networks (CVNNs) with time delays via the pinning control method. Different from general control schemes, the pinning control is beneficial to reduce the control cost by pinning the fractional nodes instead of all ones. By separating the complex-valued system into two equivalent real-valued systems and employing the Lyapunov functional as well as some inequality techniques, the asymptotic synchronization criterion is given to guarantee the realization of synchronization of memristive CVNNs. Meanwhile, sufficient conditions for exponential synchronization of the considered systems is also proposed. Finally, the validity of our proposed results is verified by a numerical example.
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Chen J, Chen B, Zeng Z. O(t -α)-synchronization and Mittag-Leffler synchronization for the fractional-order memristive neural networks with delays and discontinuous neuron activations. Neural Netw 2018; 100:10-24. [PMID: 29427959 DOI: 10.1016/j.neunet.2018.01.004] [Citation(s) in RCA: 36] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/25/2017] [Revised: 11/16/2017] [Accepted: 01/18/2018] [Indexed: 11/26/2022]
Abstract
This paper investigates O(t-α)-synchronization and adaptive Mittag-Leffler synchronization for the fractional-order memristive neural networks with delays and discontinuous neuron activations. Firstly, based on the framework of Filippov solution and differential inclusion theory, using a Razumikhin-type method, some sufficient conditions ensuring the global O(t-α)-synchronization of considered networks are established via a linear-type discontinuous control. Next, a new fractional differential inequality is established and two new discontinuous adaptive controller is designed to achieve Mittag-Leffler synchronization between the drive system and the response systems using this inequality. Finally, two numerical simulations are given to show the effectiveness of the theoretical results. Our approach and theoretical results have a leading significance in the design of synchronized fractional-order memristive neural networks circuits involving discontinuous activations and time-varying delays.
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Affiliation(s)
- Jiejie Chen
- College of Computer Science and Technology, Hubei Normal University, Huangshi 435002, Hubei, China; School of Automation, Huazhong University of Science and Technology, Wuhan 430074, China.
| | - Boshan Chen
- College of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, Hubei, China.
| | - Zhigang Zeng
- School of Automation, Huazhong University of Science and Technology, Wuhan 430074, China; Key Laboratory of Image Processing and Intelligent Control of Education Ministry of China, Wuhan 430074, China.
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Chen J, Chen B, Zeng Z. Global Uniform Asymptotic Fixed Deviation Stability and Stability for Delayed Fractional-order Memristive Neural Networks with Generic Memductance. Neural Netw 2018; 98:65-75. [DOI: 10.1016/j.neunet.2017.11.004] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/22/2017] [Revised: 10/16/2017] [Accepted: 11/02/2017] [Indexed: 10/18/2022]
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Finite-time stability for memristor based switched neural networks with time-varying delays via average dwell time approach. Neurocomputing 2018. [DOI: 10.1016/j.neucom.2017.10.003] [Citation(s) in RCA: 28] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Bao G, Zeng Z. Region stability analysis for switched discrete-time recurrent neural network with multiple equilibria. Neurocomputing 2017. [DOI: 10.1016/j.neucom.2017.03.065] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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Di Marco M, Forti M, Pancioni L. Memristor standard cellular neural networks computing in the flux-charge domain. Neural Netw 2017; 93:152-164. [PMID: 28599148 DOI: 10.1016/j.neunet.2017.05.009] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/09/2017] [Revised: 03/21/2017] [Accepted: 05/10/2017] [Indexed: 10/19/2022]
Abstract
The paper introduces a class of memristor neural networks (NNs) that are characterized by the following salient features. (a) The processing of signals takes place in the flux-charge domain and is based on the time evolution of memristor charges. The processing result is given by the constant asymptotic values of charges that are stored in the memristors acting as non-volatile memories in steady state. (b) The dynamic equations describing the memristor NNs in the flux-charge domain are analogous to those describing, in the traditional voltage-current domain, the dynamics of a standard (S) cellular (C) NN, and are implemented by using a realistic model of memristors as that proposed by HP. This analogy makes it possible to use the bulk of results in the SCNN literature for designing memristor NNs to solve processing tasks in real time. Convergence of memristor NNs in the presence of multiple asymptotically stable equilibrium points is addressed and some applications to image processing tasks are presented to illustrate the real-time processing capabilities. Computing in the flux-charge domain is shown to have significant advantages with respect to computing in the voltage-current domain. One advantage is that, when a steady state is reached, currents, voltages and hence power in a memristor NN vanish, whereas memristors keep in memory the processing result. This is basically different from SCNNs for which currents, voltages and power do not vanish at a steady state, and batteries are needed to keep in memory the processing result.
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Affiliation(s)
- Mauro Di Marco
- Department of Information Engineering and Mathematics, University of Siena, 53100 Siena, Italy.
| | - Mauro Forti
- Department of Information Engineering and Mathematics, University of Siena, 53100 Siena, Italy.
| | - Luca Pancioni
- Department of Information Engineering and Mathematics, University of Siena, 53100 Siena, Italy.
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Feng J, Ma Q, Qin S. Exponential Stability of Periodic Solution for Impulsive Memristor-Based Cohen–Grossberg Neural Networks with Mixed Delays. INT J PATTERN RECOGN 2017. [DOI: 10.1142/s0218001417500227] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
Memristor, as the future of artificial intelligence, has been widely used in pattern recognition or signal processing from sensor arrays. Memristor-based recurrent neural network (MRNN) is an ideal model to mimic the functionalities of the human brain due to the physical properties of memristor. In this paper, the periodicity for memristor-based Cohen–Grossberg neural networks (MCGNNs) is studied. The neural network (NN) considered in this paper is based on the memristor and involves time-varying delays, distributed delays and impulsive effects. The boundedness and monotonicity of the activation function are not assumed. By some inequality technique and contraction mapping principle, we prove the existence, uniqueness and exponential stability of periodic solution for MCGNNs. Finally, some numeral examples and comparisons are provided to illustrate the validation of our results.
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Affiliation(s)
- Jiqiang Feng
- Institute of Intelligent Computing Science, Shenzhen University, Shenzhen 518060, P. R. China
| | - Qiang Ma
- Department of Mathematics, Harbin Institute of Technology, Weihai 264209, P. R. China
| | - Sitian Qin
- Department of Mathematics, Harbin Institute of Technology, Weihai 264209, P. R. China
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Jiang P, Zeng Z, Chen J. On the periodic dynamics of memristor-based neural networks with leakage and time-varying delays. Neurocomputing 2017. [DOI: 10.1016/j.neucom.2016.09.029] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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Xu C, Li P, Pang Y. Exponential Stability of Almost Periodic Solutions for Memristor-Based Neural Networks with Distributed Leakage Delays. Neural Comput 2016; 28:2726-2756. [DOI: 10.1162/neco_a_00895] [Citation(s) in RCA: 60] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/04/2022]
Abstract
In this letter, we deal with a class of memristor-based neural networks with distributed leakage delays. By applying a new Lyapunov function method, we obtain some sufficient conditions that ensure the existence, uniqueness, and global exponential stability of almost periodic solutions of neural networks. We apply the results of this solution to prove the existence and stability of periodic solutions for this delayed neural network with periodic coefficients. We then provide an example to illustrate the effectiveness of the theoretical results. Our results are completely new and complement the previous studies Chen, Zeng, and Jiang ( 2014 ) and Jiang, Zeng, and Chen ( 2015 ).
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Affiliation(s)
- Changjin Xu
- Guizhou Key Laboratory of Economics System Simulation, Guizhou University of Finance and Economics, Guiyang 550004, P.R. China
| | - Peiluan Li
- School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, P.R. China
| | - Yicheng Pang
- School of Mathematics and Statistics, Guizhou University of Finance and Economics Guiyang 550004, P.R. China
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Almost Periodic Dynamics for Memristor-Based Shunting Inhibitory Cellular Neural Networks with Leakage Delays. COMPUTATIONAL INTELLIGENCE AND NEUROSCIENCE 2016; 2016:3587271. [PMID: 27840634 PMCID: PMC5090130 DOI: 10.1155/2016/3587271] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 05/16/2016] [Accepted: 07/31/2016] [Indexed: 11/17/2022]
Abstract
We investigate a class of memristor-based shunting inhibitory cellular neural networks with leakage delays. By applying a new Lyapunov function method, we prove that the neural network which has a unique almost periodic solution is globally exponentially stable. Moreover, the theoretical findings of this paper on the almost periodic solution are applied to prove the existence and stability of periodic solution for memristor-based shunting inhibitory cellular neural networks with leakage delays and periodic coefficients. An example is given to illustrate the effectiveness of the theoretical results. The results obtained in this paper are completely new and complement the previously known studies of Wu (2011) and Chen and Cao (2002).
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Rakkiyappan R, Udhaya Kumari E, Chandrasekar A, Krishnasamy R. Synchronization and periodicity of coupled inertial memristive neural networks with supremums. Neurocomputing 2016. [DOI: 10.1016/j.neucom.2016.06.061] [Citation(s) in RCA: 59] [Impact Index Per Article: 7.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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15
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Novel Switching Jumps Dependent Exponential Synchronization Criteria for Memristor-Based Neural Networks. Neural Process Lett 2016. [DOI: 10.1007/s11063-016-9504-3] [Citation(s) in RCA: 38] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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16
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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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17
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Abdurahman A, Jiang H, Teng Z. Finite-time synchronization for memristor-based neural networks with time-varying delays. Neural Netw 2015; 69:20-8. [DOI: 10.1016/j.neunet.2015.04.015] [Citation(s) in RCA: 159] [Impact Index Per Article: 17.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/17/2014] [Revised: 02/10/2015] [Accepted: 04/24/2015] [Indexed: 11/16/2022]
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Jiang P, Zeng Z, Chen J. Almost periodic solutions for a memristor-based neural networks with leakage, time-varying and distributed delays. Neural Netw 2015; 68:34-45. [DOI: 10.1016/j.neunet.2015.04.005] [Citation(s) in RCA: 37] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/10/2014] [Revised: 02/10/2015] [Accepted: 04/14/2015] [Indexed: 11/28/2022]
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Stochastic exponential synchronization control of memristive neural networks with multiple time-varying delays. Neurocomputing 2015. [DOI: 10.1016/j.neucom.2015.03.069] [Citation(s) in RCA: 52] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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