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Wei Y, Zhou S, Chen Y, Cao J. Explicit stability condition for delta fractional order systems with α∈(0,+∞). ISA TRANSACTIONS 2024; 150:121-133. [PMID: 38744609 DOI: 10.1016/j.isatra.2024.04.032] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/05/2023] [Revised: 04/18/2024] [Accepted: 04/27/2024] [Indexed: 05/16/2024]
Abstract
This paper delves into the stability of time-advance delta fractional order systems, with a specific emphasis on the order range (0,+∞) rather than the conventional range (0,1). The delta Laplace transform is used to investigate the stability of the suggested system, and a mapping relation ρ=ss+1 is introduced. The explicit stability condition is provided, articulated in relation to a specific distribution of eigenvalues of the system matrix. To validate this condition, the paper establishes equivalence between the delta difference and the nabla difference. Furthermore, both quantitative and qualitative analyses are conducted on the range of the unstable region. Finally, the correctness of the developed results is validated by three examples.
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Affiliation(s)
- Yiheng Wei
- School of Mathematics, Southeast University, Nanjing 211189, China.
| | - Shuaiyu Zhou
- School of Mathematics, Southeast University, Nanjing 211189, China
| | - YangQuan Chen
- School of Engineering, University of California, Merced, CA 95343, USA
| | - Jinde Cao
- School of Mathematics, Southeast University, Nanjing 211189, China; Ahlia University, Manama 10878, Bahrain
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2
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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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3
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Liu CG, Wang JL, Wu HN. Finite-Time Passivity for Coupled Fractional-Order Neural Networks With Multistate or Multiderivative Couplings. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2023; 34:5976-5987. [PMID: 34928805 DOI: 10.1109/tnnls.2021.3132069] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
This article mainly delves into the finite-time passivity (FTP) for coupled fractional-order neural networks with multistate couplings (CFNNMSCs) or coupled fractional-order neural networks with multiderivative couplings (CFNNMDCs). Distinguishing from the traditional FTP definitions, several concepts of FTP for fractional-order systems are given. On one hand, we present several sufficient conditions to ensure the FTP for CFNNMSCs by artfully designing a state-feedback controller and an adaptive state-feedback controller. On the other hand, by utilizing some inequality techniques, two sets of FTP criteria for CFNNMDCs are also established on the basis of the state-feedback and adaptive state-feedback controllers. Finally, numerical examples are used to demonstrate the validity of the derived FTP criteria.
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4
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Li B, Cheng X. Synchronization analysis of coupled fractional-order neural networks with time-varying delays. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2023; 20:14846-14865. [PMID: 37679162 DOI: 10.3934/mbe.2023665] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/09/2023]
Abstract
In this paper, the complete synchronization and Mittag-Leffler synchronization problems of a kind of coupled fractional-order neural networks with time-varying delays are introduced and studied. First, the sufficient conditions for a controlled system to reach complete synchronization are established by using the Kronecker product technique and Lyapunov direct method under pinning control. Here the pinning controller only needs to control part of the nodes, which can save more resources. To make the system achieve complete synchronization, only the error system is stable. Next, a new adaptive feedback controller is designed, which combines the Razumikhin-type method and Mittag-Leffler stability theory to make the controlled system realize Mittag-Leffler synchronization. The controller has time delays, and the calculation can be simplified by constructing an appropriate auxiliary function. Finally, two numerical examples are given. The simulation process shows that the conditions of the main theorems are not difficult to obtain, and the simulation results confirm the feasibility of the theorems.
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Affiliation(s)
- Biwen Li
- School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China
| | - Xuan Cheng
- 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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6
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Bifurcation Mechanism for Fractional-Order Three-Triangle Multi-delayed Neural Networks. Neural Process Lett 2022. [DOI: 10.1007/s11063-022-11130-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
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7
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Naz S, Raja MAZ, Mehmood A, Jaafery AZ. Intelligent Predictive Solution Dynamics for Dahl Hysteresis Model of Piezoelectric Actuator. MICROMACHINES 2022; 13:2205. [PMID: 36557504 PMCID: PMC9785130 DOI: 10.3390/mi13122205] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/12/2022] [Revised: 12/05/2022] [Accepted: 12/09/2022] [Indexed: 06/17/2023]
Abstract
Piezoelectric actuated models are promising high-performance precision positioning devices used for broad applications in the field of precision machines and nano/micro manufacturing. Piezoelectric actuators involve a nonlinear complex hysteresis that may cause degradation in performance. These hysteresis effects of piezoelectric actuators are mathematically represented as a second-order system using the Dahl hysteresis model. In this paper, artificial intelligence-based neurocomputing feedforward and backpropagation networks of the Levenberg-Marquardt method (LMM-NNs) and Bayesian Regularization method (BRM-NNs) are exploited to examine the numerical behavior of the Dahl hysteresis model representing a piezoelectric actuator, and the Adams numerical scheme is used to create datasets for various cases. The generated datasets were used as input target values to the neural network to obtain approximated solutions and optimize the values by using backpropagation neural networks of LMM-NNs and BRM-NNs. The performance analysis of LMM-NNs and BRM-NNs of the Dahl hysteresis model of the piezoelectric actuator is validated through convergence curves and accuracy measures via mean squared error and regression analysis.
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Affiliation(s)
- Sidra Naz
- Department of Electrical Engineering, Pakistan Institute of Engineering and Applied Sciences, Islamabad 45650, Pakistan
| | - Muhammad Asif Zahoor Raja
- Future Technology Research Center, National Yunlin University of Science and Technology, Yunlin 64002, Taiwan
| | - Ammara Mehmood
- School of Engineering, RMIT University, Melbourne 3001, Australia
| | - Aneela Zameer Jaafery
- Department of Computer and Information Sciences, Pakistan Institute of Engineering and Applied Sciences, Islamabad 45650, Pakistan
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8
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Delay-dependent and Order-dependent Conditions for Stability and Stabilization of Fractional-order Memristive Neural Networks with Time-varying Delays. Neurocomputing 2022. [DOI: 10.1016/j.neucom.2022.12.006] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
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9
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Li H, Kao Y, Bao H, Chen Y. Uniform Stability of Complex-Valued Neural Networks of Fractional Order With Linear Impulses and Fixed Time Delays. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2022; 33:5321-5331. [PMID: 33852395 DOI: 10.1109/tnnls.2021.3070136] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
As a generation of the real-valued neural network (RVNN), complex-valued neural network (CVNN) is based on the complex-valued (CV) parameters and variables. The fractional-order (FO) CVNN with linear impulses and fixed time delays is discussed. By using the sign function, the Banach fixed point theorem, and two classes of activation functions, some criteria of uniform stability for the solution and existence and uniqueness for equilibrium solution are derived. Finally, three experimental simulations are presented to illustrate the correctness and effectiveness of the obtained results.
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10
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Zhang F, Zeng Z. Multistability and Stabilization of Fractional-Order Competitive Neural Networks With Unbounded Time-Varying Delays. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2022; 33:4515-4526. [PMID: 33630741 DOI: 10.1109/tnnls.2021.3057861] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
This article investigates the multistability and stabilization of fractional-order competitive neural networks (FOCNNs) with unbounded time-varying delays. By utilizing the monotone operator, several sufficient conditions of the coexistence of equilibrium points (EPs) are obtained for FOCNNs with concave-convex activation functions. And then, the multiple μ -stability of delayed FOCNNs is derived by the analytical method. Meanwhile, several comparisons with existing work are shown, which implies that the derived results cover the inverse-power stability and Mittag-Leffler stability as special cases. Moreover, the criteria on the stabilization of FOCNNs with uncertainty are established by designing a controller. Compared with the results of fractional-order neural networks, the obtained results in this article enrich and improve the previous results. Finally, three numerical examples are provided to show the effectiveness of the presented results.
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11
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Gu Y, Wang H, Yu Y. Stability and synchronization of fractional-order generalized reaction–diffusion neural networks with multiple time delays and parameter mismatch. Neural Comput Appl 2022. [DOI: 10.1007/s00521-022-07414-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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12
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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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13
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Luo S, Lewis FL, Song Y, Ouakad HM. Optimal Synchronization of Unidirectionally Coupled FO Chaotic Electromechanical Devices With the Hierarchical Neural Network. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2022; 33:1192-1202. [PMID: 33296315 DOI: 10.1109/tnnls.2020.3041350] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
This article solves the problem of optimal synchronization, which is important but challenging for coupled fractional-order (FO) chaotic electromechanical devices composed of mechanical and electrical oscillators and electromagnetic filed by using a hierarchical neural network structure. The synchronization model of the FO electromechanical devices with capacitive and resistive couplings is built, and the phase diagrams reveal that the dynamic properties are closely related to sets of physical parameters, coupling coefficients, and FOs. To force the slave system to move from its original orbits to the orbits of the master system, an optimal synchronization policy, which includes an adaptive neural feedforward policy and an optimal neural feedback policy, is proposed. The feedforward controller is developed in the framework of FO backstepping integrated with the hierarchical neural network to estimate unknown functions of dynamic system in which the mentioned network has the formula transformation and hierarchical form to reduce the numbers of weights and membership functions. Also, an adaptive dynamic programming (ADP) policy is proposed to address the zero-sum differential game issue in the optimal neural feedback controller in which the hierarchical neural network is designed to yield solutions of the constrained Hamilton-Jacobi-Isaacs (HJI) equation online. The presented scheme not only ensures uniform ultimate boundedness of closed-loop coupled FO chaotic electromechanical devices and realizes optimal synchronization but also achieves a minimum value of cost function. Simulation results further show the validity of the presented scheme.
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14
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Suresh R, Syed Ali M, Saroha S. Global exponential stability of memristor based uncertain neural networks with time-varying delays via Lagrange sense. J EXP THEOR ARTIF IN 2022. [DOI: 10.1080/0952813x.2021.1960632] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
Affiliation(s)
- R. Suresh
- Department of Mathematics, Sri Venkateswara College of Engineering, Sriperumbudur, India
| | - M. Syed Ali
- Department of Mathematics, Thiruvalluvar University, Vellore, India
| | - Sumit Saroha
- Department of Electrical Engineering, Guru Jambheswar University of Science and Technology, Hisar, India
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15
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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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16
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Bifurcation Study for Fractional-Order Three-Layer Neural Networks Involving Four Time Delays. Cognit Comput 2022. [DOI: 10.1007/s12559-021-09939-1] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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17
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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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18
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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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Adaptive Event-Triggered Synchronization of Uncertain Fractional Order Neural Networks with Double Deception Attacks and Time-Varying Delay. ENTROPY 2021; 23:e23101291. [PMID: 34682015 PMCID: PMC8535153 DOI: 10.3390/e23101291] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 09/07/2021] [Revised: 09/24/2021] [Accepted: 09/25/2021] [Indexed: 11/17/2022]
Abstract
This paper investigates the problem of adaptive event-triggered synchronization for uncertain FNNs subject to double deception attacks and time-varying delay. During network transmission, a practical deception attack phenomenon in FNNs should be considered; that is, we investigated the situation in which the attack occurs via both communication channels, from S-C and from C-A simultaneously, rather than considering only one, as in many papers; and the double attacks are described by high-level Markov processes rather than simple random variables. To further reduce network load, an advanced AETS with an adaptive threshold coefficient was first used in FNNs to deal with deception attacks. Moreover, given the engineering background, uncertain parameters and time-varying delay were also considered, and a feedback control scheme was adopted. Based on the above, a unique closed-loop synchronization error system was constructed. Sufficient conditions that guarantee the stability of the closed-loop system are ensured by the Lyapunov-Krasovskii functional method. Finally, a numerical example is presented to verify the effectiveness of the proposed method.
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20
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Cao Q, Hao H. A Chaotic Neural Network Model for English Machine Translation Based on Big Data Analysis. COMPUTATIONAL INTELLIGENCE AND NEUROSCIENCE 2021; 2021:3274326. [PMID: 34306051 PMCID: PMC8270720 DOI: 10.1155/2021/3274326] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/02/2021] [Revised: 06/21/2021] [Accepted: 06/26/2021] [Indexed: 11/22/2022]
Abstract
In this paper, the chaotic neural network model of big data analysis is used to conduct in-depth analysis and research on the English translation. Firstly, under the guidance of the translation strategy of text type theory, the translation generated by the machine translation system is edited after translation, and then professionals specializing in computer and translation are invited to confirm the translation. After that, the errors in the translations generated by the machine translation system are classified based on the Double Quantum Filter-Muttahida Quami Movement (DQF-MQM) error type classification framework. Due to the characteristics of the source text as an informative academic text, long and difficult sentences, passive voice, and terminology translation are the main causes of machine translation errors. In view of the rigorous logic of the source text and the fixed language steps, this research proposes corresponding post-translation editing strategies for each type of error. It is suggested that translators should maintain the logic of the source text by converting implicit connections into explicit connections, maintain the academic accuracy of the source text by adding subjects and adjusting the word order to deal with the passive voice, and deal with semitechnical terms by appropriately selecting word meanings in postediting. The errors of machine translation in computer science and technology text abstracts are systematically categorized, and the corresponding post-translation editing strategies are proposed to provide reference suggestions for translators in this field, to improve the quality of machine translation in this field.
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Affiliation(s)
- Qianyu Cao
- School of Foreign Languages, Chengdu University of Information Technology, Chengdu 610036, China
| | - Hanmei Hao
- Chengdu Angke Technologies Co., Ltd., Chengdu 610000, China
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21
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Aravind RV, Balasubramaniam P. Stochastic stability of fractional-order Markovian jumping complex-valued neural networks with time-varying delays. Neurocomputing 2021. [DOI: 10.1016/j.neucom.2021.01.053] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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22
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Niu L, Xu W, Guo Q. Transient response of the time-delay system excited by Gaussian noise based on complex fractional moments. CHAOS (WOODBURY, N.Y.) 2021; 31:053111. [PMID: 34240926 DOI: 10.1063/5.0033593] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/17/2020] [Accepted: 04/20/2021] [Indexed: 06/13/2023]
Abstract
In this paper, the transient response of the time-delay system under additive and multiplicative Gaussian white noise is investigated. Based on the approximate transformation method, we convert the time-delay system into an equivalent system without time delay. The one-dimensional Ito stochastic differential equation with respect to the amplitude response is derived by the stochastic averaging method, and Mellin transformation is utilized to transform the related Fokker-Planck-Kolmogorov equation in the real numbers field into a first-order ordinary differential equation (ODE) of complex fractional moments (CFM) in the complex number field. By solving the ODE of CFM, the transient probability density function can be constructed. Numerical methods are used to ascertain the effectiveness of the CFM method, the effects of system parameters on system response and the level of error vary with time as well as noise intensity are investigated. In addition, the CFM method is first implemented to analyze transient bifurcation, and the relation between CFM and bifurcation is discussed for the first time. Furthermore, the imperfect symmetry property appear on the projection map of joint probability density function.
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Affiliation(s)
- Lizhi Niu
- Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710129, People's Republic of China
| | - Wei Xu
- Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710129, People's Republic of China
| | - Qin Guo
- Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710129, People's Republic of China
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23
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Békollè D, Ezzinbi K, Fatajou S, Houpa Danga DE, Béssémè FM. Attractiveness of pseudo almost periodic solutions for delayed cellular neural networks in the context of measure theory. Neurocomputing 2021. [DOI: 10.1016/j.neucom.2020.12.047] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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24
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Kao Y, Li Y, Park JH, Chen X. Mittag-Leffler Synchronization of Delayed Fractional Memristor Neural Networks via Adaptive Control. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2021; 32:2279-2284. [PMID: 32479403 DOI: 10.1109/tnnls.2020.2995718] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
This brief is devoted to exploring the global Mittag-Leffler (ML) synchronization problem of fractional-order memristor neural networks (FOMNNs) with leakage delay via a hybrid adaptive controller. By applying Fillipov's theory and the Lyapunov functional method, the novel algebraic sufficient condition for the global ML synchronization of FOMNNs is derived. Finally, a simulation example is presented to show the practicability of our findings.
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Bifurcations Induced by Self-connection Delay in High-Order Fractional Neural Networks. Neural Process Lett 2021. [DOI: 10.1007/s11063-020-10395-5] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/17/2023]
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26
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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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Wang L, Wu J, Wang X. Finite-Time Stabilization of Memristive Neural Networks with Time Delays. Neural Process Lett 2020. [DOI: 10.1007/s11063-020-10390-w] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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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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Waseem W, Sulaiman M, Aljohani AJ. Investigation of fractional models of damping material by a neuroevolutionary approach. CHAOS, SOLITONS & FRACTALS 2020. [DOI: 10.1016/j.chaos.2020.110198] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/08/2023]
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Jia J, Zeng Z. LMI-based criterion for global Mittag-Leffler lag quasi-synchronization of fractional-order memristor-based neural networks via linear feedback pinning control. Neurocomputing 2020. [DOI: 10.1016/j.neucom.2020.05.074] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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Wu Q, Song Q, Hu B, Zhao Z, Liu Y, Alsaadi FE. Robust stability of uncertain fractional order singular systems with neutral and time-varying delays. Neurocomputing 2020. [DOI: 10.1016/j.neucom.2020.03.015] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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Xu C, Liao M, Li P, Liu Z. Anti-periodic Oscillations of Fuzzy Delayed Cellular Neural Networks with Impulse on Time Scales. Neural Process Lett 2020. [DOI: 10.1007/s11063-020-10203-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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34
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Quantized Control for Synchronization of Delayed Fractional-Order Memristive Neural Networks. Neural Process Lett 2020. [DOI: 10.1007/s11063-020-10259-y] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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Xie YK, Lu JW, Meng B, Wang Z. Stability analysis for a new fractional order N species network. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2020; 17:2805-2819. [PMID: 32987497 DOI: 10.3934/mbe.2020154] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
The present paper considers a fractional-order N species network, in which, the general functions are used for finding general theories. The existence, uniqueness, and non-negativity of the solutions for the considered model are proved. Moreover, the local and global asymptotic stability of the equilibrium point are studied by using eigenvalue method and Lyapunov direct method. Finally, some simple examples and numerical simulations are provided to demonstrate the theoretical results.
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Affiliation(s)
- Ying Kang Xie
- College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China
| | - Jun Wei Lu
- School of Electrical and Automation Engineering, Nanjing Normal University, Nanjing 210023, China
| | - Bo Meng
- College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China
| | - Zhen Wang
- College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao 266590, China
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Meng F, Li K, Zhao Z, Song Q, Liu Y, Alsaadi FE. Periodicity of impulsive Cohen–Grossberg-type fuzzy neural networks with hybrid delays. Neurocomputing 2019. [DOI: 10.1016/j.neucom.2019.08.057] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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37
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Huang C, Nie X, Zhao X, Song Q, Tu Z, Xiao M, Cao J. Novel bifurcation results for a delayed fractional-order quaternion-valued neural network. Neural Netw 2019; 117:67-93. [DOI: 10.1016/j.neunet.2019.05.002] [Citation(s) in RCA: 64] [Impact Index Per Article: 12.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/16/2019] [Revised: 05/04/2019] [Accepted: 05/06/2019] [Indexed: 11/16/2022]
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