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Huang C, Mo S, Cao J. Detections of bifurcation in a fractional-order Cohen-Grossberg neural network with multiple delays. Cogn Neurodyn 2024; 18:1379-1396. [PMID: 38826673 PMCID: PMC11143155 DOI: 10.1007/s11571-023-09934-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/10/2021] [Revised: 12/25/2022] [Accepted: 01/24/2023] [Indexed: 03/06/2023] Open
Abstract
The dynamics of integer-order Cohen-Grossberg neural networks with time delays has lately drawn tremendous attention. It reveals that fractional calculus plays a crucial role on influencing the dynamical behaviors of neural networks (NNs). This paper deals with the problem of the stability and bifurcation of fractional-order Cohen-Grossberg neural networks (FOCGNNs) with two different leakage delay and communication delay. The bifurcation results with regard to leakage delay are firstly gained. Then, communication delay is viewed as a bifurcation parameter to detect the critical values of bifurcations for the addressed FOCGNN, and the communication delay induced-bifurcation conditions are procured. We further discover that fractional orders can enlarge (reduce) stability regions of the addressed FOCGNN. Furthermore, we discover that, for the same system parameters, the convergence time to the equilibrium point of FONN is shorter (longer) than that of integer-order NNs. In this paper, the present methodology to handle the characteristic equation with triple transcendental terms in delayed FOCGNNs is concise, neoteric and flexible in contrast with the prior mechanisms owing to skillfully keeping away from the intricate classified discussions. Eventually, the developed analytic results are nicely showcased by the simulation examples.
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Affiliation(s)
- Chengdai Huang
- School of Mathematics and Statistics, Xinyang Normal University, Xinyang, 464000 China
| | - Shansong Mo
- School of Mathematics and Statistics, Xinyang Normal University, Xinyang, 464000 China
| | - Jinde Cao
- School of Mathematics, Southeast University, Nanjing, 210096 China
- Yonsei Frontier Lab, Yonsei University, Seoul, 03722 South Korea
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2
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Kang Q, Yang Q, Yang J, Gan Q, Li R. Synchronization in Finite-Time of Delayed Fractional-Order Fully Complex-Valued Dynamical Networks via Non-Separation Method. ENTROPY (BASEL, SWITZERLAND) 2022; 24:1460. [PMID: 37420480 DOI: 10.3390/e24101460] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/02/2022] [Revised: 09/23/2022] [Accepted: 10/08/2022] [Indexed: 07/09/2023]
Abstract
The finite-time synchronization (FNTS) problem for a class of delayed fractional-order fully complex-valued dynamic networks (FFCDNs) with internal delay and non-delayed and delayed couplings is studied by directly constructing Lyapunov functions instead of decomposing the original complex-valued networks into two real-valued networks. Firstly, a mixed delay fractional-order mathematical model is established for the first time as fully complex-valued, where the outer coupling matrices of the model are not restricted to be identical, symmetric, or irreducible. Secondly, to overcome the limitation of the use range of a single controller, two delay-dependent controllers are designed based on the complex-valued quadratic norm and the norm composed of its real and imaginary parts' absolute values, respectively, to improve the synchronization control efficiency. Besides, the relationships between the fractional order of the system, the fractional-order power law, and the settling time (ST) are analyzed. Finally, the feasibility and effectiveness of the control method designed in this paper are verified by numerical simulation.
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Affiliation(s)
- Qiaokun Kang
- Shijiazhuang Campus, Army Engineering University, Shijiazhuang 050003, China
| | - Qingxi Yang
- Shijiazhuang Campus, Army Engineering University, Shijiazhuang 050003, China
| | - Jing Yang
- Shijiazhuang Campus, Army Engineering University, Shijiazhuang 050003, China
| | - Qintao Gan
- Shijiazhuang Campus, Army Engineering University, Shijiazhuang 050003, China
| | - Ruihong Li
- Shijiazhuang Campus, Army Engineering University, Shijiazhuang 050003, China
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3
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Gan Q, Li L, Yang J, Qin Y, Meng M. Improved Results on Fixed-/Preassigned-Time Synchronization for Memristive Complex-Valued Neural Networks. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2022; 33:5542-5556. [PMID: 33852405 DOI: 10.1109/tnnls.2021.3070966] [Citation(s) in RCA: 11] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
This article concerns the problems of synchronization in a fixed time or prespecified time for memristive complex-valued neural networks (MCVNNs), in which the state variables, activation functions, rates of neuron self-inhibition, neural connection memristive weights, and external inputs are all assumed to be complex-valued. First, the more comprehensive fixed-time stability theorem and more accurate estimations on settling time (ST) are systematically established by using the comparison principle. Second, by introducing different norms of complex numbers instead of decomposing the complex-valued system into real and imaginary parts, we successfully design several simpler discontinuous controllers to acquire much improved fixed-time synchronization (FXTS) results. Third, based on similar mathematical derivations, the preassigned-time synchronization (PATS) conditions are explored by newly developed new control strategies, in which ST can be prespecified and is independent of initial values and any parameters of neural networks and controllers. Finally, numerical simulations are provided to illustrate the effectiveness and superiority of the improved synchronization methodology.
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A Novel English Translation Model in Complex Environments Using Two-Stream Convolutional Neural Networks. JOURNAL OF ENVIRONMENTAL AND PUBLIC HEALTH 2022; 2022:8426460. [PMID: 36105512 PMCID: PMC9467711 DOI: 10.1155/2022/8426460] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/15/2022] [Revised: 08/04/2022] [Accepted: 08/06/2022] [Indexed: 11/18/2022]
Abstract
Although translation is an essential component of learning English, it does not receive the attention it merits in the modern English classroom. Teachers and students primarily emphasize listening, reading, and writing while neglecting the development of translation skills. The English test in China now reflects the fact that there are now very specific requirements for students' translation skills. As a result, we should emphasize developing students' translation skills when teaching them English. The following experimental data can be obtained following the study and experiment on the English translation simulation model based on the two-stream convolutional neural network: English vocabulary and grammar have passing and excellent rates of 90 and 57 percent, respectively, while reading has passing and excellent rates of 69 and 8 percent, respectively. The ability of students to translate into English has significantly improved after using the English translation simulation model based on the two-stream convolutional neural network.
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5
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Liu A, Zhao H, Wang Q, Niu S, Gao X, Chen C, Li L. A new predefined-time stability theorem and its application in the synchronization of memristive complex-valued BAM neural networks. Neural Netw 2022; 153:152-163. [PMID: 35724477 DOI: 10.1016/j.neunet.2022.05.031] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/23/2022] [Revised: 05/24/2022] [Accepted: 05/31/2022] [Indexed: 11/17/2022]
Abstract
In this paper, two novel and general predefined-time stability lemmas are given and applied to the predefined-time synchronization problem of memristive complex-valued bidirectional associative memory neural networks (MCVBAMNNs). Firstly, different from the generally fixed-time stability lemma, the setting of an adjustable time parameter in the derived predefined-time stability lemma causes it to be more flexible and more general. Secondly, the model studied in the complex-valued BAM neural networks model, which is different from the previous discussion of the real part and imaginary part respectively. It is more practical to study the complex-valued nonseparation. Thirdly, two effective controllers are designed to realize the synchronization performance of BAM neural networks based on the predefined-time stability, and the analysis is given based on general predefined-time synchronization. Finally, the correctness of the theoretical derivation is verified by numerical simulation. A secure communication scheme based on predefined-time synchronization of MCVBAMNNs is proposed, and the effectiveness and superiority of the results are proved.
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Affiliation(s)
- Aidi Liu
- Shandong Provincial Key Laboratory of Network Based Intelligent Computing, School of Information Science and Engineering, University of Jinan, Jinan 250022, China
| | - Hui Zhao
- Shandong Provincial Key Laboratory of Network Based Intelligent Computing, School of Information Science and Engineering, University of Jinan, Jinan 250022, China.
| | - Qingjie Wang
- Shandong Provincial Key Laboratory of Network Based Intelligent Computing, School of Information Science and Engineering, University of Jinan, Jinan 250022, China
| | - Sijie Niu
- Shandong Provincial Key Laboratory of Network Based Intelligent Computing, School of Information Science and Engineering, University of Jinan, Jinan 250022, China
| | - Xizhan Gao
- Shandong Provincial Key Laboratory of Network Based Intelligent Computing, School of Information Science and Engineering, University of Jinan, Jinan 250022, China
| | - Chuan Chen
- Shandong Provincial Key Laboratory of Computer Networks, Shandong Computer Science Center (National Supercomputer Center in Jinan), School of Cyber Security, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China
| | - Lixiang Li
- Information Security Center, State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100876, China
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Global Exponential Stability of Fractional Order Complex-Valued Neural Networks with Leakage Delay and Mixed Time Varying Delays. FRACTAL AND FRACTIONAL 2022. [DOI: 10.3390/fractalfract6030140] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/10/2022]
Abstract
This paper investigates the global exponential stability of fractional order complex-valued neural networks with leakage delay and mixed time varying delays. By constructing a proper Lyapunov-functional we established sufficient conditions to ensure global exponential stability of the fractional order complex-valued neural networks. The stability conditions are established in terms of linear matrix inequalities. Finally, two numerical examples are given to illustrate the effectiveness of the obtained results.
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7
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Lag projective synchronization of nonidentical fractional delayed memristive neural networks. Neurocomputing 2022. [DOI: 10.1016/j.neucom.2021.10.061] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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8
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Viera-Martin E, Gómez-Aguilar JF, Solís-Pérez JE, Hernández-Pérez JA, Escobar-Jiménez RF. Artificial neural networks: a practical review of applications involving fractional calculus. THE EUROPEAN PHYSICAL JOURNAL. SPECIAL TOPICS 2022; 231:2059-2095. [PMID: 35194484 PMCID: PMC8853315 DOI: 10.1140/epjs/s11734-022-00455-3] [Citation(s) in RCA: 11] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/07/2021] [Accepted: 01/13/2022] [Indexed: 05/13/2023]
Abstract
In this work, a bibliographic analysis on artificial neural networks (ANNs) using fractional calculus (FC) theory has been developed to summarize the main features and applications of the ANNs. ANN is a mathematical modeling tool used in several sciences and engineering fields. FC has been mainly applied on ANNs with three different objectives, such as systems stabilization, systems synchronization, and parameters training, using optimization algorithms. FC and some control strategies have been satisfactorily employed to attain the synchronization and stabilization of ANNs. To show this fact, in this manuscript are summarized, the architecture of the systems, the control strategies, and the fractional derivatives used in each research work, also, the achieved goals are presented. Regarding the parameters training using optimization algorithms issue, in this manuscript, the systems types, the fractional derivatives involved, and the optimization algorithm employed to train the ANN parameters are also presented. In most of the works found in the literature where ANNs and FC are involved, the authors focused on controlling the systems using synchronization and stabilization. Furthermore, recent applications of ANNs with FC in several fields such as medicine, cryptographic, image processing, robotic are reviewed in detail in this manuscript. Works with applications, such as chaos analysis, functions approximation, heat transfer process, periodicity, and dissipativity, also were included. Almost to the end of the paper, several future research topics arising on ANNs involved with FC are recommended to the researchers community. From the bibliographic review, we concluded that the Caputo derivative is the most utilized derivative for solving problems with ANNs because its initial values take the same form as the differential equations of integer-order.
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Affiliation(s)
- E. Viera-Martin
- Tecnológico Nacional de México/CENIDET, Interior Internado Palmira S/N, Col. Palmira, C.P. 62490 Cuernavaca, Morelos Mexico
| | - J. F. Gómez-Aguilar
- CONACyT-Tecnológico Nacional de México/CENIDET, Interior Internado Palmira S/N, Col. Palmira, C.P. 62490 Cuernavaca, Morelos Mexico
| | - J. E. Solís-Pérez
- Escuela Nacional de Estudios Superiores Unidad Juriquilla, Universidad Nacional Autónoma de México, Boulevard Juriquilla 3001, Juriquilla La Mesa, C.P. 76230 Juriquilla, Querétaro Mexico
| | - J. A. Hernández-Pérez
- Universidad Autónoma del Estado de Morelos/Centro de Investigación en Ingeniería y Ciencias Aplicadas, Av. Universidad No. 1001, Col Chamilpa, C.P. 62209 Cuernavaca, Morelos Mexico
| | - R. F. Escobar-Jiménez
- Tecnológico Nacional de México/CENIDET, Interior Internado Palmira S/N, Col. Palmira, C.P. 62490 Cuernavaca, Morelos Mexico
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9
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Jin W, Cui W, Wang Z. Finite-time Synchronization of fractional-order complex-valued fuzzy cellular neural networks with time-varying delays. JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2021. [DOI: 10.3233/jifs-211183] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
Finite-time synchronization is concerned for the fractional-order complex-valued fuzzy cellular neural networks (FOCVFCNNs) with leakage delay and time-varying delays. Without using the usual complex-valued system decomposition method, this paper designs the different forms of the controllers by using 2-norm. And we construct the appropriate Lyapunov functional and apply inequality analytical techniques, some new sufficient conditions are obtained to ensure finite-time synchronization of the FOCVFCNNs. The upper bound of setting-time function is obtained. Finally, numerical examples are examined to illustrate the effectiveness of the analytical results.
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Affiliation(s)
- Wenbin Jin
- School of Mathematics Physics and Statistics, Shanghai University of Engineering Science, Shanghai, China
| | - Wenxia Cui
- School of Mathematics Physics and Statistics, Shanghai University of Engineering Science, Shanghai, China
| | - Zhenjie Wang
- School of Mathematics Physics and Statistics, Shanghai University of Engineering Science, Shanghai, China
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10
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Wei F, Chen G, Wang W. Finite-time stabilization of memristor-based inertial neural networks with time-varying delays combined with interval matrix method. Knowl Based Syst 2021. [DOI: 10.1016/j.knosys.2021.107395] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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11
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Du F, Lu JG. New Criteria on Finite-Time Stability of Fractional-Order Hopfield Neural Networks With Time Delays. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2021; 32:3858-3866. [PMID: 32822312 DOI: 10.1109/tnnls.2020.3016038] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
In this article, the finite-time stability (FTS) of fractional-order Hopfield neural networks with time delays (FHNNTDs) is studied. A widely used inequality in investigating the stability of the fractional-order neural networks is fractional-order Gronwall inequality related to the Mittag-Leffler function, which cannot be directly used to study the stability of the factional-order neural networks with time delays. In the existing works related to fractional-order Gronwall inequality with time delays, the order was divided into two cases: λ ∈ (0,0.5] and λ ∈ (0.5,+∞) . In this article, a new fractional-order Gronwall integral inequality with time delay and the unified form for all the fractional order is developed, which can be widely applied to investigate FTS of various fractional-order systems with time delays. Based on this new inequality, a new criterion for the FTS of FHNNTDs is derived. Compared with the existing criteria, in which fractional order λ ∈ (0,1) was divided into two cases, λ ∈ (0,0.5] and λ ∈ (0.5,1) , the obtained results in this article are presented in the unified form of fractional order λ ∈ (0,1) and convenient to verify. More importantly, the criteria in this article are less conservative than some existing ones. Finally, two numerical examples are given to demonstrate the validity of the proposed results.
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12
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Abstract
This paper expounds the bifurcations of two-delayed fractional-order neural networks (FONNs) with multiple neurons. Leakage delay or communication delay is viewed as a bifurcation parameter, stability zones and bifurcation conditions with respect to them are commendably established, respectively. It declares that both leakage delay and communication delay immensely influence the stability and bifurcation of the developed FONNs. The explored FONNs illustrate superior stability performance if selecting a lesser leakage delay or communication delay, and Hopf bifurcation generates once they overstep their critical values. The verification of the feasibility of the developed analytic results is implemented via numerical experiments.
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Affiliation(s)
- Chengdai Huang
- School of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, P. R. China
| | - Jinde Cao
- School of Mathematics, Southeast University, Nanjing 210096, P. R. China
- Yonsei Frontier Lab, Yonsei University, Seoul 03722, South Korea
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13
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Yang Z, Zhang J, Hu J, Mei J. New results on finite-time stability for fractional-order neural networks with proportional delay. Neurocomputing 2021. [DOI: 10.1016/j.neucom.2021.02.082] [Citation(s) in RCA: 15] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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14
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singh A, Rai JN. Stability of Fractional Order Fuzzy Cellular Neural Networks with Distributed Delays via Hybrid Feedback Controllers. Neural Process Lett 2021. [DOI: 10.1007/s11063-021-10460-7] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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15
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New criteria for finite-time stability of fractional order memristor-based neural networks with time delays. Neurocomputing 2021. [DOI: 10.1016/j.neucom.2020.09.039] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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16
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Huang C, Liu H, Shi X, Chen X, Xiao M, Wang Z, Cao J. Bifurcations in a fractional-order neural network with multiple leakage delays. Neural Netw 2020; 131:115-126. [DOI: 10.1016/j.neunet.2020.07.015] [Citation(s) in RCA: 23] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/15/2020] [Revised: 07/06/2020] [Accepted: 07/10/2020] [Indexed: 10/23/2022]
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17
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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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18
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Finite-Time Mittag–Leffler Synchronization of Neutral-Type Fractional-Order Neural Networks with Leakage Delay and Time-Varying Delays. MATHEMATICS 2020. [DOI: 10.3390/math8071146] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
This paper studies fractional-order neural networks with neutral-type delay, leakage delay, and time-varying delays. A sufficient condition which ensures the finite-time synchronization of these networks based on a state feedback control scheme is deduced using the generalized Gronwall–Bellman inequality. Then, a different state feedback control scheme is employed to realize the finite-time Mittag–Leffler synchronization of these networks by using the fractional-order extension of the Lyapunov direct method for Mittag–Leffler stability. Two numerical examples illustrate the feasibility and the effectiveness of the deduced sufficient criteria.
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19
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Finite time anti-synchronization of complex-valued neural networks with bounded asynchronous time-varying delays. Neurocomputing 2020. [DOI: 10.1016/j.neucom.2020.01.035] [Citation(s) in RCA: 20] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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20
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You X, Song Q, Zhao Z. Existence and finite-time stability of discrete fractional-order complex-valued neural networks with time delays. Neural Netw 2020; 123:248-260. [DOI: 10.1016/j.neunet.2019.12.012] [Citation(s) in RCA: 24] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/27/2019] [Revised: 11/28/2019] [Accepted: 12/10/2019] [Indexed: 10/25/2022]
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21
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He J, Chen F, Lei T, Bi Q. Global adaptive matrix-projective synchronization of delayed fractional-order competitive neural network with different time scales. Neural Comput Appl 2020. [DOI: 10.1007/s00521-020-04728-7] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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22
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Zheng B, Hu C, Yu J, Jiang H. Finite-time synchronization of fully complex-valued neural networks with fractional-order. Neurocomputing 2020. [DOI: 10.1016/j.neucom.2019.09.048] [Citation(s) in RCA: 34] [Impact Index Per Article: 8.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
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23
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Finite-Time Mittag-Leffler Stability of Fractional-Order Quaternion-Valued Memristive Neural Networks with Impulses. Neural Process Lett 2019. [DOI: 10.1007/s11063-019-10154-1] [Citation(s) in RCA: 52] [Impact Index Per Article: 10.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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24
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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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25
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Ding D, Yao X, Zhang H. Complex Projection Synchronization of Fractional-Order Complex-Valued Memristive Neural Networks with Multiple Delays. Neural Process Lett 2019. [DOI: 10.1007/s11063-019-10093-x] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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26
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Wang H, Tan J, Huang T, Duan S. Impulsive delayed integro-differential inequality and its application on IMNNs with discrete and distributed delays. Neurocomputing 2019. [DOI: 10.1016/j.neucom.2019.03.007] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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27
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Hu T, He Z, Zhang X, Zhong S. Global synchronization of time-invariant uncertainty fractional-order neural networks with time delay. Neurocomputing 2019. [DOI: 10.1016/j.neucom.2019.02.020] [Citation(s) in RCA: 21] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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28
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Zhang W, Zhang H, Cao J, Alsaadi FE, Chen D. Synchronization in uncertain fractional-order memristive complex-valued neural networks with multiple time delays. Neural Netw 2019; 110:186-198. [DOI: 10.1016/j.neunet.2018.12.004] [Citation(s) in RCA: 55] [Impact Index Per Article: 11.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/23/2018] [Revised: 10/13/2018] [Accepted: 12/04/2018] [Indexed: 11/16/2022]
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29
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Li HL, Cao J, Jiang H, Alsaedi A. Finite-time synchronization of fractional-order complex networks via hybrid feedback control. Neurocomputing 2018. [DOI: 10.1016/j.neucom.2018.09.021] [Citation(s) in RCA: 36] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
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30
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Finite-time synchronization for delayed complex-valued neural networks via integrating inequality method. Neurocomputing 2018. [DOI: 10.1016/j.neucom.2018.08.063] [Citation(s) in RCA: 56] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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31
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The stability of memristive multidirectional associative memory neural networks with time-varying delays in the leakage terms via sampled-data control. PLoS One 2018; 13:e0204002. [PMID: 30248118 PMCID: PMC6152966 DOI: 10.1371/journal.pone.0204002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/27/2017] [Accepted: 08/31/2018] [Indexed: 11/19/2022] Open
Abstract
In this paper, we propose a new model of memristive multidirectional associative memory neural networks, which concludes the time-varying delays in leakage terms via sampled-data control. We use the input delay method to turn the sampling system into a continuous time-delaying system. Then we analyze the exponential stability and asymptotic stability of the equilibrium points for this model. By constructing a suitable Lyapunov function, using the Lyapunov stability theorem and some inequality techniques, some sufficient criteria for ensuring the stability of equilibrium points are obtained. Finally, numerical examples are given to demonstrate the effectiveness of our results.
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32
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Thuan MV, Huong DC, Hong DT. New Results on Robust Finite-Time Passivity for Fractional-Order Neural Networks with Uncertainties. Neural Process Lett 2018. [DOI: 10.1007/s11063-018-9902-9] [Citation(s) in RCA: 27] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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Wu X, Feng J, Nie Z. Pinning complex-valued complex network via aperiodically intermittent control. Neurocomputing 2018. [DOI: 10.1016/j.neucom.2018.03.055] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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Robust finite-time state estimation for uncertain discrete-time Markovian jump neural networks with two delay components. Neurocomputing 2018. [DOI: 10.1016/j.neucom.2017.12.047] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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Li L, Wang Z, Lu J, Li Y. Adaptive Synchronization of Fractional-Order Complex-Valued Neural Networks with Discrete and Distributed Delays. ENTROPY (BASEL, SWITZERLAND) 2018; 20:E124. [PMID: 33265215 PMCID: PMC7512617 DOI: 10.3390/e20020124] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 01/25/2018] [Revised: 02/10/2018] [Accepted: 02/11/2018] [Indexed: 11/22/2022]
Abstract
In this paper, the synchronization problem of fractional-order complex-valued neural networks with discrete and distributed delays is investigated. Based on the adaptive control and Lyapunov function theory, some sufficient conditions are derived to ensure the states of two fractional-order complex-valued neural networks with discrete and distributed delays achieve complete synchronization rapidly. Finally, numerical simulations are given to illustrate the effectiveness and feasibility of the theoretical results.
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Affiliation(s)
- Li Li
- College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China
| | - Zhen Wang
- College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China
- College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao 266590, China
| | - Junwei Lu
- School of Electrical and Automation Engineering, Nanjing Normal University, Nanjing 210023, China
| | - Yuxia Li
- College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao 266590, China
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Bao G, Zeng Z, Shen Y. Region stability analysis and tracking control of memristive recurrent neural network. Neural Netw 2018; 98:51-58. [DOI: 10.1016/j.neunet.2017.11.005] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/21/2017] [Revised: 10/05/2017] [Accepted: 11/02/2017] [Indexed: 10/18/2022]
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Robust Mittag-Leffler Synchronization for Uncertain Fractional-Order Discontinuous Neural Networks via Non-fragile Control Strategy. Neural Process Lett 2018. [DOI: 10.1007/s11063-018-9787-7] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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Tan M, Xu D. Multiple μ-stability analysis for memristor-based complex-valued neural networks with nonmonotonic piecewise nonlinear activation functions and unbounded time-varying delays. Neurocomputing 2018. [DOI: 10.1016/j.neucom.2017.11.047] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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Circuit Implementation, Synchronization of Multistability, and Image Encryption of a Four-Wing Memristive Chaotic System. JOURNAL OF ELECTRICAL AND COMPUTER ENGINEERING 2018. [DOI: 10.1155/2018/8649294] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
The four-wing memristive chaotic system used in synchronization is applied to secure communication which can increase the difficulty of deciphering effectively and enhance the security of information. In this paper, a novel four-wing memristive chaotic system with an active cubic flux-controlled memristor is proposed based on a Lorenz-like circuit. Dynamical behaviors of the memristive system are illustrated in terms of Lyapunov exponents, bifurcation diagrams, coexistence Poincaré maps, coexistence phase diagrams, and attraction basins. Besides, the modular equivalent circuit of four-wing memristive system is designed and the corresponding results are observed to verify its accuracy and rationality. A nonlinear synchronization controller with exponential function is devised to realize synchronization of the coexistence of multiple attractors, and the synchronization control scheme is applied to image encryption to improve secret key space. More interestingly, considering different influence of multistability on encryption, the appropriate key is achieved to enhance the antideciphering ability.
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