1
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He Y, Zhang W, Zhang H, Chen D, Cao J. Lag projective synchronization of discrete-time fractional-order quaternion-valued neural networks with time delays. Neural Netw 2024; 179:106532. [PMID: 39096750 DOI: 10.1016/j.neunet.2024.106532] [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: 01/08/2024] [Revised: 03/14/2024] [Accepted: 07/09/2024] [Indexed: 08/05/2024]
Abstract
This paper deals with the lag projective synchronization (LPS) problem for a class of discrete-time fractional-order quaternion-valued neural networks(DTFO QVNNs) systems with time delays. Firstly, a DTFOQVNNs system with time delay is constructed. Secondly, linear and adaptive feedback controllers with sign function are designed respectively. Furthermore, through Lyapunov direct method, DTFO inequality technique and Razumikhin theorem, some sufficiency criteria are obtained to ensure that the system in this article can achieve LPS. At last, the significance of the theoretical part of this paper is verified through numerical simulation.
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Affiliation(s)
- Yan He
- School of Mathematics and Physics, Anqing Normal University, Anqing 246133, China
| | - Weiwei Zhang
- School of Mathematics and Physics, Anqing Normal University, Anqing 246133, China; Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210093, China; Key Laboratory of Modeling, Simulation and Control of Complex Ecological model in Dabie Mountains of Anhui Higher Education Institutes, Anqing Normal University, Anqing 246011, China.
| | - Hai Zhang
- School of Mathematics and Physics, Anqing Normal University, Anqing 246133, China; Key Laboratory of Modeling, Simulation and Control of Complex Ecological model in Dabie Mountains of Anhui Higher Education Institutes, Anqing Normal University, Anqing 246011, China
| | - Dingyuan Chen
- School of Mathematics and Physics, Anqing Normal University, Anqing 246133, China
| | - Jinde Cao
- School of Mathematics, Southeast University, Nanjing 210096, China
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2
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Wang H, Gu Y, Zhang X, Yu Y. Stability and synchronization of fractional-order reaction-diffusion inertial time-delayed neural networks with parameters perturbation. Neural Netw 2024; 179:106564. [PMID: 39089150 DOI: 10.1016/j.neunet.2024.106564] [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: 03/27/2024] [Revised: 07/03/2024] [Accepted: 07/20/2024] [Indexed: 08/03/2024]
Abstract
This study is centered around the dynamic behaviors observed in a class of fractional-order generalized reaction-diffusion inertial neural networks (FGRDINNs) with time delays. These networks are characterized by differential equations involving two distinct fractional derivatives of the state. The global uniform stability of FGRDINNs with time delays is explored utilizing Lyapunov comparison principles. Furthermore, global synchronization conditions for FGRDINNs with time delays are derived through the Lyapunov direct method, with consideration given to various feedback control strategies and parameter perturbations. The effectiveness of the theoretical findings is demonstrated through three numerical examples, and the impact of controller parameters on the error system is further investigated.
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Affiliation(s)
- Hu Wang
- School of Statistics and Mathematics, Central University of Finance and Economics, Beijing, 100081, China
| | - Yajuan Gu
- School of Applied Science, Beijing Information Science and Technology University, Beijing, 100192, China
| | - Xiaoli Zhang
- School of Mathematics and Statistics, Beijing Jiaotong University, Beijing, 100044, China
| | - Yongguang Yu
- School of Mathematics and Statistics, Beijing Jiaotong University, Beijing, 100044, China.
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3
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Li HL, Cao J, Hu C, Jiang H, Alsaadi FE. Synchronization Analysis of Discrete-Time Fractional-Order Quaternion-Valued Uncertain Neural Networks. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2024; 35:14178-14189. [PMID: 37227907 DOI: 10.1109/tnnls.2023.3274959] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
This article studies synchronization issues for a class of discrete-time fractional-order quaternion-valued uncertain neural networks (DFQUNNs) using nonseparation method. First, based on the theory of discrete-time fractional calculus and quaternion properties, two equalities on the nabla Laplace transform and nabla sum are strictly proved, whereafter three Caputo difference inequalities are rigorously demonstrated. Next, based on our established inequalities and equalities, some simple and verifiable quasi-synchronization criteria are derived under the quaternion-valued nonlinear controller, and complete synchronization is achieved using quaternion-valued adaptive controller. Finally, numerical simulations are presented to substantiate the validity of derived results.
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4
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Li HL, Cao J, Hu C, Zhang L, Jiang H. Adaptive control-based synchronization of discrete-time fractional-order fuzzy neural networks with time-varying delays. Neural Netw 2023; 168:59-73. [PMID: 37742532 DOI: 10.1016/j.neunet.2023.09.019] [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: 03/04/2023] [Revised: 08/11/2023] [Accepted: 09/10/2023] [Indexed: 09/26/2023]
Abstract
This paper is concerned with complete synchronization for discrete-time fractional-order fuzzy neural networks (DFFNNs) with time-varying delays. First, three original equalities and two Caputo σ-difference inequalities are established based on theory of discrete-time fractional Calculus. Next, a novel discrete-time adaptive controller with time-varying delay is designed, by virtue of 1-norm Lyapunov function and newly established lemmas herein as well as inequality techniques and contradiction method, some judgement conditions are derived to guarantee complete synchronization for the explored DFFNNs. Benefitting from discrete-time adaptive control strategy and our analysis method, the conservatism of the derived synchronization criteria is reduced. Ultimately, the effectiveness of our theoretical results and secure communication scheme are demonstrated through two numerical examples.
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Affiliation(s)
- Hong-Li Li
- College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China; School of Mathematics, Southeast University, Nanjing 210096, China.
| | - Jinde Cao
- School of Mathematics, Southeast University, Nanjing 210096, China; Yonsei Frontier Lab, Yonsei University, Seoul 03722, South Korea.
| | - Cheng Hu
- College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China
| | - Long Zhang
- College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China
| | - Haijun Jiang
- College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China; School of Mathematics and Statistics, Yili Normal University, Yining 835000, China
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5
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Yang J, Li HL, Zhang L, Hu C, Jiang H. Synchronization of discrete-time fractional fuzzy neural networks with delays via quantized control. ISA TRANSACTIONS 2023; 141:241-250. [PMID: 37451923 DOI: 10.1016/j.isatra.2023.06.037] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/24/2022] [Revised: 06/10/2023] [Accepted: 06/30/2023] [Indexed: 07/18/2023]
Abstract
In this paper, synchronization issue of discrete-time fractional fuzzy neural networks (DFFNNs) with delays is solved via quantized control, and is applied in image encryption. Firstly, a novel fractional-order h-difference inequality which makes Lyapunov method more flexible and practical is strictly proved based on the properties of convex functions and theory of discrete fractional calculus. Secondly, by using compression mapping theorem and mathematical induction, we obtain two sufficient conditions to ensure the existence and uniqueness of solutions for DFFNNs. Whereafter, we design a suitable quantized controller, which not only saves channel resources but also reduces control costs. By utilizing our inequality and some analytical techniques, several conservative synchronization criteria for DFFNNs are acquired. Finally, two examples are arranged to illustrate the validity and practicability of our results.
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Affiliation(s)
- Jikai Yang
- College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China
| | - Hong-Li Li
- College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China; School of Mathematics, Southeast University, Nanjing 210096, China.
| | - Long Zhang
- College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China
| | - Cheng Hu
- College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China
| | - Haijun Jiang
- College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China
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6
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He S, Vignesh D, Rondoni L, Banerjee S. Chaos and multi-layer attractors in asymmetric neural networks coupled with discrete fractional memristor. Neural Netw 2023; 167:572-587. [PMID: 37708779 DOI: 10.1016/j.neunet.2023.08.041] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/24/2023] [Revised: 07/19/2023] [Accepted: 08/23/2023] [Indexed: 09/16/2023]
Abstract
This article introduces a novel model of asymmetric neural networks combined with fractional difference memristors, which has both theoretical and practical implications in the rapidly evolving field of computational intelligence. The proposed model includes two types of fractional difference memristor elements: one with hyperbolic tangent memductance and the other with periodic memductance and memristor state described by sine functions. The authenticity of the constructed memristor is confirmed through fingerprint verification. The research extensively investigates the dynamics of a coupled neural network model, analyzing its stability at equilibrium states, studying bifurcation diagrams, and calculating the largest Lyapunov exponents. The results suggest that when incorporating sine memristors, the model demonstrates coexisting state variables depending on the initial conditions, revealing the emergence of multi-layer attractors. The article further demonstrates how the memristor state shifts through numerical simulations with varying memductance values. Notably, the study emphasizes the crucial role of memductance (synaptic weight) in determining the complex dynamical characteristics of neural network systems. To support the analytical results and demonstrate the chaotic response of state variables, the article includes appropriate numerical simulations. These simulations effectively validate the presented findings and provide concrete evidence of the system's chaotic behavior.
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Affiliation(s)
- Shaobo He
- School of Automation and Electronic Information, Xiangtan University, Xiangtan, 411105, China.
| | - D Vignesh
- Department of Mathematics, School of Engineering and Technology, CMR University, Chagalahatti, Bangalore, 562149, Karnataka, India.
| | - Lamberto Rondoni
- Department of Mathematical Sciences, Giuseppe Luigi Lagrange, Politecnico di Torino, Corso Duca degli Abruzzi 24, Turin, Italy.
| | - Santo Banerjee
- Department of Mathematical Sciences, Giuseppe Luigi Lagrange, Politecnico di Torino, Corso Duca degli Abruzzi 24, Turin, Italy.
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7
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Zhang XL, Li HL, Yu Y, Zhang L, Jiang H. Quasi-projective and complete synchronization of discrete-time fractional-order delayed neural networks. Neural Netw 2023; 164:497-507. [PMID: 37201310 DOI: 10.1016/j.neunet.2023.05.005] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/17/2022] [Revised: 03/28/2023] [Accepted: 05/01/2023] [Indexed: 05/20/2023]
Abstract
This paper presents new theoretical results on quasi-projective synchronization (Q-PS) and complete synchronization (CS) of one kind of discrete-time fractional-order delayed neural networks (DFDNNs). At first, three new fractional difference inequalities for exploring the upper bound of quasi-synchronization error and adaptive synchronization are established by dint of Laplace transform and properties of discrete Mittag-Leffler function, which vastly expand a number of available results. Furthermore, two controllers are designed including nonlinear controller and adaptive controller. And on the basis of Lyapunov method, the aforementioned inequalities and properties of fractional-order difference operators, some sufficient synchronization criteria of DFDNNs are derived. Because of the above controllers, synchronization criteria in this paper are less conservative. At last, numerical examples are carried out to illustrate the usefulness of theoretical upshots.
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Affiliation(s)
- Xiao-Li Zhang
- College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China; Xinjiang Key Laboratory of Applied Mathematics, Urumqi 830017, China
| | - Hong-Li Li
- College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China; Xinjiang Key Laboratory of Applied Mathematics, Urumqi 830017, China.
| | - Yongguang Yu
- School of Mathematics and Statistics, Beijing Jiaotong University, Beijing 100044, China
| | - Long Zhang
- College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China; Xinjiang Key Laboratory of Applied Mathematics, Urumqi 830017, China
| | - Haijun Jiang
- College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China; Xinjiang Key Laboratory of Applied Mathematics, Urumqi 830017, China
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8
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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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9
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Yang D, Yu Y, Hu W, Yuan X, Ren G. Mean Square Asymptotic Stability of Discrete-Time Fractional Order Stochastic Neural Networks with Multiple Time-Varying Delays. Neural Process Lett 2023. [DOI: 10.1007/s11063-023-11200-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/03/2023]
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10
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Quasi-Projective and Mittag-Leffler Synchronization of Discrete-Time Fractional-Order Complex-Valued Fuzzy Neural Networks. Neural Process Lett 2023. [DOI: 10.1007/s11063-023-11153-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023]
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11
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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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12
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Liu A, Zhao H, Wang Q, Niu S, Gao X, Su Z, Li L. Fixed/Predefined-time synchronization of memristor-based complex-valued BAM neural networks for image protection. Front Neurorobot 2022; 16:1000426. [DOI: 10.3389/fnbot.2022.1000426] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/22/2022] [Accepted: 09/26/2022] [Indexed: 11/13/2022] Open
Abstract
This paper investigates the fixed-time synchronization and the predefined-time synchronization of memristive complex-valued bidirectional associative memory neural networks (MCVBAMNNs) with leakage time-varying delay. First, the proposed neural networks are regarded as two dynamic real-valued systems. By designing a suitable feedback controller, combined with the Lyapunov method and inequality technology, a more accurate upper bound of stability time estimation is given. Then, a predefined-time stability theorem is proposed, which can easily establish a direct relationship between tuning gain and system stability time. Any predefined time can be set as controller parameters to ensure that the synchronization error converges within the predefined time. Finally, the developed chaotic MCVBAMNNs and predefined-time synchronization technology are applied to image encryption and decryption. The correctness of the theory and the security of the cryptographic system are verified by numerical simulation.
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13
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Chen S, Li HL, Bao H, Zhang L, Jiang H, Li Z. Global Mittag–Leffler stability and synchronization of discrete-time fractional-order delayed quaternion-valued neural networks. Neurocomputing 2022. [DOI: 10.1016/j.neucom.2022.09.035] [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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14
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Narayanan G, Ali MS, Alsulami H, Saeed T, Ahmad B. Synchronization of T–S Fuzzy Fractional-Order Discrete-Time Complex-Valued Molecular Models of mRNA and Protein in Regulatory Mechanisms with Leakage Effects. Neural Process Lett 2022. [DOI: 10.1007/s11063-022-11010-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/14/2022]
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15
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Yu T, Cao J, Rutkowski L, Luo YP. Finite-Time Synchronization of Complex-Valued Memristive-Based Neural Networks via Hybrid Control. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2022; 33:3938-3947. [PMID: 33566775 DOI: 10.1109/tnnls.2021.3054967] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
The finite-time synchronization problem is investigated for the master-slave complex-valued memristive neural networks in this article. A novel Lyapunov-function based finite-time stability criterion with impulsive effects is proposed and utilized to design the decentralized finite-time synchronization controller. Not only the settling time but also the attractive domain with respect to the impulsive gain and average impulsive interval, as well as initial values is derived according to the sufficient synchronization condition. Two examples are outlined to illustrate the validity of our hybrid control strategy.
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16
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Yu T, Wang H, Cao J, Xue C. Finite-time stabilization of memristive neural networks via two-phase method. Neurocomputing 2022. [DOI: 10.1016/j.neucom.2022.03.059] [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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17
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On Variable-Order Fractional Discrete Neural Networks: Solvability and Stability. FRACTAL AND FRACTIONAL 2022. [DOI: 10.3390/fractalfract6020119] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/10/2022]
Abstract
Few papers have been published to date regarding the stability of neural networks described by fractional difference operators. This paper makes a contribution to the topic by presenting a variable-order fractional discrete neural network model and by proving its Ulam–Hyers stability. In particular, two novel theorems are illustrated, one regarding the existence of the solution for the proposed variable-order network and the other regarding its Ulam–Hyers stability. Finally, numerical simulations of three-dimensional and two-dimensional variable-order fractional neural networks were carried out to highlight the effectiveness of the conceived theoretical approach.
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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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19
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Asymptotic Stabilization of Delayed Linear Fractional-Order Systems Subject to State and Control Constraints. FRACTAL AND FRACTIONAL 2022. [DOI: 10.3390/fractalfract6020067] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
Studies have shown that fractional calculus can describe and characterize a practical system satisfactorily. Therefore, the stabilization of fractional-order systems is of great significance. The asymptotic stabilization problem of delayed linear fractional-order systems (DLFS) subject to state and control constraints is studied in this article. Firstly, the existence conditions for feedback controllers of DLFS subject to both state and control constraints are given. Furthermore, a sufficient condition for invariance of polyhedron set is established by using invariant set theory. A new Lyapunov function is constructed on the basis of the constraints, and some sufficient conditions for the asymptotic stability of DLFS are obtained. Then, the feedback controller and the corresponding solution algorithms are given to ensure the asymptotic stability under state and control input constraints. The proposed solution algorithm transforms the asymptotic stabilization problem into a linear/nonlinear programming (LP/NP) problem which is easy to solve from the perspective of computation. Finally, three numerical examples are offered to illustrate the effectiveness of the proposed method.
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20
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Extreme Multistability of a Fractional-Order Discrete-Time Neural Network. FRACTAL AND FRACTIONAL 2021. [DOI: 10.3390/fractalfract5040202] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
At present, the extreme multistability of fractional order neural networks are gaining much interest from researchers. In this paper, by utilizing the fractional ℑ-Caputo operator, a simple fractional order discrete-time neural network with three neurons is introduced. The dynamic of this model are experimentally investigated via the maximum Lyapunov exponent, phase portraits, and bifurcation diagrams. Numerical simulation demonstrates that the new network has various types of coexisting attractors. Moreover, it is of note that the interesting phenomena of extreme multistability is discovered, i.e., the coexistence of symmetric multiple attractors.
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21
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Finite-Time Projective Synchronization of Caputo Type Fractional Complex-Valued Delayed Neural Networks. MATHEMATICS 2021. [DOI: 10.3390/math9121406] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
This paper focuses on investigating the finite-time projective synchronization of Caputo type fractional-order complex-valued neural networks with time delay (FOCVNNTD). Based on the properties of fractional calculus and various inequality techniques, by constructing suitable the Lyapunov function and designing two new types controllers, i.e., feedback controller and adaptive controller, two sufficient criteria are derived to ensure the projective finite-time synchronization between drive and response systems, and the synchronization time can effectively be estimated. Finally, two numerical examples are presented to verify the effectiveness and feasibility of the proposed results.
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22
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Synchronization analysis for discrete fractional-order complex-valued neural networks with time delays. Neural Comput Appl 2021. [DOI: 10.1007/s00521-021-05808-y] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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23
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Wu X, Liu S, Wang Y. Stability analysis of Riemann-Liouville fractional-order neural networks with reaction-diffusion terms and mixed time-varying delays. Neurocomputing 2021. [DOI: 10.1016/j.neucom.2020.12.053] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/01/2022]
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24
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Shao S, Liu X, Cao J. Prespecified-time synchronization of switched coupled neural networks via smooth controllers. Neural Netw 2020; 133:32-39. [PMID: 33125916 DOI: 10.1016/j.neunet.2020.10.007] [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: 04/21/2020] [Revised: 08/18/2020] [Accepted: 10/12/2020] [Indexed: 10/23/2022]
Abstract
This paper considers the prespecified-time synchronization issue of switched coupled neural networks (SCNNs) under some smooth controllers. Different from the traditional finite-time synchronization (FTS), the synchronization time obtained in this paper is independent of control gains, initial values or network topology, which can be pre-set as to the task requirements. Moreover, unlike the existing nonsmooth or even discontinuous FTS control strategies, the new proposed control protocols are fully smooth, which abandon the common fractional power feedbacks or signum functions. Finally, two illustrative examples are provided to illustrate the effectiveness of the theoretical results.
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Affiliation(s)
- Shao Shao
- Research Center for Complex Networks & Swarm Intelligence, School of Computer Science & Technology, Jiangsu Normal University, Xuzhou 221116, China
| | - Xiaoyang Liu
- Research Center for Complex Networks & Swarm Intelligence, School of Computer Science & Technology, Jiangsu Normal University, Xuzhou 221116, China.
| | - Jinde Cao
- School of Mathematics, Southeast University, Nanjing 210096, China; Yonsei Frontier Lab, Yonsei University, Seoul, Korea.
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25
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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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