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Cao J, Udhayakumar K, Rakkiyappan R, Li X, Lu J. A Comprehensive Review of Continuous-/Discontinuous-Time Fractional-Order Multidimensional Neural Networks. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2023; 34:5476-5496. [PMID: 34962883 DOI: 10.1109/tnnls.2021.3129829] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
The dynamical study of continuous-/discontinuous-time fractional-order neural networks (FONNs) has been thoroughly explored, and several publications have been made available. This study is designed to give an exhaustive review of the dynamical studies of multidimensional FONNs in continuous/discontinuous time, including Hopfield NNs (HNNs), Cohen-Grossberg NNs, and bidirectional associative memory NNs, and similar models are considered in real ( [Formula: see text]), complex ( [Formula: see text]), quaternion ( [Formula: see text]), and octonion ( [Formula: see text]) fields. Since, in practice, delays are unavoidable, theoretical findings from multidimensional FONNs with various types of delays are thoroughly evaluated. Some required and adequate stability and synchronization requirements are also mentioned for fractional-order NNs without delays.
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2
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Ding Z, Yang L, Ye Y, Li S, Huang Z. Passivity and passification of fractional-order memristive neural networks with time delays. ISA TRANSACTIONS 2023; 137:314-322. [PMID: 36746695 DOI: 10.1016/j.isatra.2023.01.034] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/21/2021] [Revised: 12/23/2022] [Accepted: 01/27/2023] [Indexed: 06/04/2023]
Abstract
A class of fractional-order memristive neural networks (FMNNs) with time delays is studied. At first, the original network system is converted to fractional-order uncertain one to simplify the analysis by a variable transformation. Successively, some new LMIs-based passivity criteria are derived by differential inclusions, set-valued maps, inequality techniques and linear matrix inequality approach. Furthermore, a feedback control protocol is designed to solve the passification problem for the considered system, whose feedback control effect on different neurons can be changed artificially, which can be better applied to neural networks. The obtained results include some existing ones as special cases. A numerical example is proposed to illustrate the theoretical results.
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Affiliation(s)
- Zhixia Ding
- School of Electrical and Information Engineering, Wuhan Institute of Technology, Wuhan 430205, China.
| | - Le Yang
- School of Electrical and Information Engineering, Wuhan Institute of Technology, Wuhan 430205, China.
| | - Yanyan Ye
- School of Automation, Guangdong University of Technology, Guangzhou 510006, China.
| | - Sai Li
- School of Electrical and Information Engineering, Wuhan Institute of Technology, Wuhan 430205, China.
| | - Zixin Huang
- School of Electrical and Information Engineering, Wuhan Institute of Technology, Wuhan 430205, China.
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3
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Zhang B, Zhang JE. Fixed-deviation stabilization and synchronization for delayed fractional-order complex-valued neural networks. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2023; 20:10244-10263. [PMID: 37322931 DOI: 10.3934/mbe.2023449] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/17/2023]
Abstract
In this paper, we study fixed-deviation stabilization and synchronization for fractional-order complex-valued neural networks with delays. By applying fractional calculus and fixed-deviation stability theory, sufficient conditions are given to ensure the fixed-deviation stabilization and synchronization for fractional-order complex-valued neural networks under the linear discontinuous controller. Finally, two simulation examples are presented to show the validity of theoretical results.
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Affiliation(s)
- Bingrui Zhang
- School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China
| | - Jin-E Zhang
- School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China
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Wang J, Zhu S, Liu X, Wen S. Mittag-Leffler stability of fractional-order quaternion-valued memristive neural networks with generalized piecewise constant argument. Neural Netw 2023; 162:175-185. [PMID: 36907007 DOI: 10.1016/j.neunet.2023.02.030] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/30/2022] [Revised: 01/28/2023] [Accepted: 02/21/2023] [Indexed: 03/06/2023]
Abstract
This paper studies the global Mittag-Leffler (M-L) stability problem for fractional-order quaternion-valued memristive neural networks (FQVMNNs) with generalized piecewise constant argument (GPCA). First, a novel lemma is established, which is used to investigate the dynamic behaviors of quaternion-valued memristive neural networks (QVMNNs). Second, by using the theories of differential inclusion, set-valued mapping, and Banach fixed point, several sufficient criteria are derived to ensure the existence and uniqueness (EU) of the solution and equilibrium point for the associated systems. Then, by constructing Lyapunov functions and employing some inequality techniques, a set of criteria are proposed to ensure the global M-L stability of the considered systems. The obtained results in this paper not only extends previous works, but also provides new algebraic criteria with a larger feasible range. Finally, two numerical examples are introduced to illustrate the effectiveness of the obtained results.
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Affiliation(s)
- Jingjing 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.
| | - 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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5
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Finite/fixed-time synchronization of memristive neural networks via event-triggered control. Knowl Based Syst 2022. [DOI: 10.1016/j.knosys.2022.110013] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
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6
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Stability of Memristor-based Fractional-order Neural Networks with Mixed Time-delay and Impulsive. Neural Process Lett 2022. [DOI: 10.1007/s11063-022-11061-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/01/2022]
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7
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Synchronization of Fractional Order Uncertain BAM Competitive Neural Networks. FRACTAL AND FRACTIONAL 2021. [DOI: 10.3390/fractalfract6010014] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
This article examines the drive-response synchronization of a class of fractional order uncertain BAM (Bidirectional Associative Memory) competitive neural networks. By using the differential inclusions theory, and constructing a proper Lyapunov-Krasovskii functional, novel sufficient conditions are obtained to achieve global asymptotic stability of fractional order uncertain BAM competitive neural networks. This novel approach is based on the linear matrix inequality (LMI) technique and the derived conditions are easy to verify via the LMI toolbox. Moreover, numerical examples are presented to show the feasibility and effectiveness of the theoretical results.
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Zhang F, Zeng Z. Multiple Mittag-Leffler Stability of Delayed Fractional-Order Cohen-Grossberg Neural Networks via Mixed Monotone Operator Pair. IEEE TRANSACTIONS ON CYBERNETICS 2021; 51:6333-6344. [PMID: 31995512 DOI: 10.1109/tcyb.2019.2963034] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
This article mainly investigates the multiple Mittag-Leffler stability of delayed fractional-order Cohen-Grossberg neural networks with time-varying delays. By using mixed monotone operator pair, the conditions of the coexistence of multiple equilibrium points are obtained for fractional-order Cohen-Grossberg neural networks, and these conditions are eventually transformed into algebraic inequalities based on the vertex of the divided region. In particular, when the symbols of these inequalities are determined by the dominant term, several verifiable corollaries are given. And then, the sufficient conditions of the Mittag-Leffler stability are derived for fractional-order Cohen-Grossberg neural networks with time-varying delays. In addition, two numerical examples are provided to illustrate the effectiveness of the theoretical results.
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Chen J, Chen B, Zeng Z. Basic theorem and global exponential stability of differential-algebraic neural networks with delay. Neural Netw 2021; 140:336-343. [PMID: 33915455 DOI: 10.1016/j.neunet.2021.01.017] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/22/2020] [Revised: 12/06/2020] [Accepted: 01/19/2021] [Indexed: 11/19/2022]
Abstract
A differential-algebraic neural network (DANN) with delay (DDANN) is proposed. Firstly, the global existence and uniqueness theorems are established for a DDANN, respectively. Next, a new differential-algebraic inequality is established. Then, a theorem on global exponential stability of DDANN is shown by using this inequality. As an application of DDANN, a very concise criterion on global exponential stability for a neutral-type neural network is given by using DDANNs. Finally, two examples are given to illustrate the theoretical results.
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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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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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Sheng Y, Huang T, Zeng Z, Li P. Exponential Stabilization of Inertial Memristive Neural Networks With Multiple Time Delays. IEEE TRANSACTIONS ON CYBERNETICS 2021; 51:579-588. [PMID: 31689230 DOI: 10.1109/tcyb.2019.2947859] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
This article investigates the global exponential stabilization (GES) of inertial memristive neural networks with discrete and distributed time-varying delays (DIMNNs). By introducing the inertial term into memristive neural networks (MNNs), DIMNNs are formulated as the second-order differential equations with discontinuous right-hand sides. Via a variable transformation, the initial DIMNNs are rewritten as the first-order differential equations. By exploiting the theories of differential inclusion, inequality techniques, and the comparison strategy, the p th moment GES ( p ≥ 1 ) of the addressed DIMNNs is presented in terms of algebraic inequalities within the sense of Filippov, which enriches and extends some published results. In addition, the global exponential stability of MNNs is also performed in the form of an M-matrix, which contains some existing ones as special cases. Finally, two simulations are carried out to validate the correctness of the theories, and an application is developed in pseudorandom number generation.
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Zhang F, Zeng Z. Multistability of Fractional-Order Neural Networks With Unbounded Time-Varying Delays. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2021; 32:177-187. [PMID: 32203030 DOI: 10.1109/tnnls.2020.2977994] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
This article addresses the multistability and attraction of fractional-order neural networks (FONNs) with unbounded time-varying delays. Several sufficient conditions are given to ensure the coexistence of equilibrium points (EPs) of FONNs with concave-convex activation functions. Moreover, by exploiting the analytical method and the property of the Mittag-Leffler function, it is shown that the multiple Mittag-Leffler stability of delayed FONNs is derived and the obtained criteria do not depend on differentiable time-varying delays. In particular, the criterion of the Mittag-Leffler stability can be simplified to M-matrix. In addition, the estimation of attraction basin of delayed FONNs is studied, which implies that the extension of attraction basin is independent of the magnitude of delays. Finally, three numerical examples are given to show the validity of the theoretical results.
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Chen J, Chen B, Zeng Z. Synchronization and Consensus in Networks of Linear Fractional-Order Multi-Agent Systems via Sampled-Data Control. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2020; 31:2955-2964. [PMID: 31502992 DOI: 10.1109/tnnls.2019.2934648] [Citation(s) in RCA: 16] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
This article addresses synchronization and consensus problems in networks of linear fractional-order multi-agent systems (LFOMAS) via sampled-data control. First, under very mild assumptions, the necessary and sufficient conditions are obtained for achieving synchronization in networks of LFOMAS. Second, the results of synchronization are applied to solve some consensus problems in networks of LFOMAS. In the obtained results, the coupling matrix does not have to be a Laplacian matrix, its off-diagonal elements do not have to be nonnegative, and its row-sum can be nonzero. Finally, the validity of the theoretical results is verified by three simulation examples.
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Jia J, Huang X, Li Y, Cao J, Alsaedi A. Global Stabilization of Fractional-Order Memristor-Based Neural Networks With Time Delay. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2020; 31:997-1009. [PMID: 31170083 DOI: 10.1109/tnnls.2019.2915353] [Citation(s) in RCA: 27] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/16/2023]
Abstract
This paper addresses the global stabilization of fractional-order memristor-based neural networks (FMNNs) with time delay. The voltage threshold type memristor model is considered, and the FMNNs are represented by fractional-order differential equations with discontinuous right-hand sides. Then, the problem is addressed based on fractional-order differential inclusions and set-valued maps, together with the aid of Lyapunov functions and the comparison principle. Two types of control laws (delayed state feedback control and coupling state feedback control) are designed. Accordingly, two types of stabilization criteria [algebraic form and linear matrix inequality (LMI) form] are established. There are two groups of adjustable parameters included in the delayed state feedback control, which can be selected flexibly to achieve the desired global asymptotic stabilization or global Mittag-Leffler stabilization. Since the existing LMI-based stability analysis techniques for fractional-order systems are not applicable to delayed fractional-order nonlinear systems, a fractional-order differential inequality is established to overcome this difficulty. Based on the coupling state feedback control, some LMI stabilization criteria are developed for the first time with the help of the newly established fractional-order differential inequality. The obtained LMI results provide new insights into the research of delayed fractional-order nonlinear systems. Finally, three numerical examples are presented to illustrate the effectiveness of the proposed theoretical results.
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15
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Delay-dependent stability analysis of the QUAD vector field fractional order quaternion-valued memristive uncertain neutral type leaky integrator echo state neural networks. Neural Netw 2019; 117:307-327. [DOI: 10.1016/j.neunet.2019.05.015] [Citation(s) in RCA: 29] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/29/2018] [Revised: 03/22/2019] [Accepted: 05/20/2019] [Indexed: 11/17/2022]
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16
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Asymptotical Stability of Riemann–Liouville Fractional-Order Neutral-Type Delayed Projective Neural Networks. Neural Process Lett 2019. [DOI: 10.1007/s11063-019-10050-8] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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17
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Samli R, Senan S, Yucel E, Orman Z. Some generalized global stability criteria for delayed Cohen-Grossberg neural networks of neutral-type. Neural Netw 2019; 116:198-207. [PMID: 31121418 DOI: 10.1016/j.neunet.2019.04.023] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/05/2019] [Revised: 04/01/2019] [Accepted: 04/30/2019] [Indexed: 10/26/2022]
Abstract
This paper carries out a theoretical investigation into the stability problem for the class of neutral-type Cohen-Grossberg neural networks with discrete time delays in states and discrete neutral delays in time derivative of states. By employing a more general type of suitable Lyapunov functional, a set of new generalized sufficient criteria are derived for the global asymptotic stability of delayed neural networks of neutral-type. The proposed stability criteria are independently of the values of the time delays and neutral delays, and they completely rely on some algebraic mathematical relationships involving the values of the elements of the interconnection matrices and the other network parameters. Therefore, it is easy to verify the validity of the obtained results by simply using some algebraic equations representing the stability conditions. A detailed comparison between our proposed results and recently reported corresponding stability results is made, proving that the results given in this paper generalize previously published stability results. A constructive numerical example is also given to demonstrate the applicability of the results of the paper.
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Affiliation(s)
- Ruya Samli
- Department of Computer Engineering, Faculty of Engineering, Istanbul University-Cerrahpasa, 34320 Avcilar, Istanbul, Turkey.
| | - Sibel Senan
- Department of Computer Engineering, Faculty of Engineering, Istanbul University-Cerrahpasa, 34320 Avcilar, Istanbul, Turkey.
| | - Eylem Yucel
- Department of Computer Engineering, Faculty of Engineering, Istanbul University-Cerrahpasa, 34320 Avcilar, Istanbul, Turkey.
| | - Zeynep Orman
- Department of Computer Engineering, Faculty of Engineering, Istanbul University-Cerrahpasa, 34320 Avcilar, Istanbul, Turkey.
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Liu W, Jiang M, Yan M. Stability analysis of memristor-based time-delay fractional-order neural networks. Neurocomputing 2019. [DOI: 10.1016/j.neucom.2018.09.073] [Citation(s) in RCA: 16] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
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19
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New conditions for global stability of neutral-type delayed Cohen–Grossberg neural networks. Neural Netw 2018; 106:1-7. [DOI: 10.1016/j.neunet.2018.06.009] [Citation(s) in RCA: 31] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/30/2018] [Accepted: 06/13/2018] [Indexed: 11/20/2022]
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