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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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2
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He J, Xiao M, Zhao J, Wang Z, Yao Y, Cao J. Tree-structured neural networks: Spatiotemporal dynamics and optimal control. Neural Netw 2023; 164:395-407. [PMID: 37172459 DOI: 10.1016/j.neunet.2023.04.039] [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: 12/27/2022] [Revised: 03/29/2023] [Accepted: 04/20/2023] [Indexed: 05/15/2023]
Abstract
How the network topology drives the response dynamic is a basic question that has not yet been fully answered in neural networks. Elucidating the internal relation between topological structures and dynamics is instrumental in our understanding of brain function. Recent studies have revealed that the ring structure and star structure have a great influence on the dynamical behavior of neural networks. In order to further explore the role of topological structures in the response dynamic, we construct a new tree structure that differs from the ring structure and star structure of traditional neural networks. Considering the diffusion effect, we propose a diffusion neural network model with binary tree structure and multiple delays. How to design control strategies to optimize brain function has also been an open question. Thus, we put forward a novel full-dimensional nonlinear state feedback control strategy to optimize relevant neurodynamics. Some conditions about the local stability and Hopf bifurcation are obtained, and it is proved that the Turing instability does not occur. Moreover, for the formation of the spatially homogeneous periodic solution, some diffusion conditions are also fused together. Finally, several numerical examples are carried out to illustrate the results' correctness. Meanwhile, some comparative experiments are rendered to reveal the effectiveness of the proposed control strategy.
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Affiliation(s)
- Jiajin He
- College of Automation & College of Artificial Intelligence, Nanjing University of Posts and Telecommunications, Nanjing 210023, Jiangsu, China.
| | - Min Xiao
- College of Automation & College of Artificial Intelligence, Nanjing University of Posts and Telecommunications, Nanjing 210023, Jiangsu, China.
| | - Jing Zhao
- College of Automation & College of Artificial Intelligence, Nanjing University of Posts and Telecommunications, Nanjing 210023, Jiangsu, China.
| | - Zhengxin Wang
- School of Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, China.
| | - Yi Yao
- School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, 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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Narayanan G, Syed Ali M, Karthikeyan R, Rajchakit G, Jirawattanapanit A. Impulsive control strategies of mRNA and protein dynamics on fractional-order genetic regulatory networks with actuator saturation and its oscillations in repressilator model. Biomed Signal Process Control 2023. [DOI: 10.1016/j.bspc.2023.104576] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023]
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4
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Cao Y, Kao Y, Park JH, Bao H. Global Mittag-Leffler Stability of the Delayed Fractional-Coupled Reaction-Diffusion System on Networks Without Strong Connectedness. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2022; 33:6473-6483. [PMID: 34081585 DOI: 10.1109/tnnls.2021.3080830] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
In this article, we mainly consider the existence of solutions and global Mittag-Leffler stability of delayed fractional-order coupled reaction-diffusion neural networks without strong connectedness. Using the Leary-Schauder's fixed point theorem and the Lyapunov method, some criteria for the existence of solutions and global Mittag-Leffler stability are given. Finally, the correctness of the theory is verified by a numerical example.
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5
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Novel controller design for finite-time synchronization of fractional-order memristive neural networks. Neurocomputing 2022. [DOI: 10.1016/j.neucom.2022.09.118] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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6
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Impulsive Security Control for Fractional-Order Delayed Multi-Agent Systems with Uncertain Parameters and Switching Topology under DoS Attack. Inf Sci (N Y) 2022. [DOI: 10.1016/j.ins.2022.10.123] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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7
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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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Abd Latiff FN, Mior Othman WA. Implementation of synchronization of multi-fractional-order of chaotic neural networks with a variety of multi-time-delays: Studying the effect of double encryption for text encryption. PLoS One 2022; 17:e0270402. [PMID: 35776758 PMCID: PMC9249245 DOI: 10.1371/journal.pone.0270402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/26/2022] [Accepted: 06/09/2022] [Indexed: 11/28/2022] Open
Abstract
This research proposes the idea of double encryption, which is the combination of chaos synchronization of non-identical multi-fractional-order neural networks with multi-time-delays (FONNSMD) and symmetric encryption. Symmetric encryption is well known to be outstanding in speed and accuracy but less effective. Therefore, to increase the strength of data protection effectively, we combine both methods where the secret keys are generated from the third part of the neural network systems (NNS) and used only once to encrypt and decrypt the message. In addition, a fractional-order Lyapunov direct function (FOLDF) is designed and implemented in sliding mode control systems (SMCS) to maintain the convergence of approximated synchronization errors. Finally, three examples are carried out to confirm the theoretical analysis and find which synchronization is achieved. Then the result is combined with symmetric encryption to increase the security of secure communication, and a numerical simulation verifies the method's accuracy.
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Affiliation(s)
- Fatin Nabila Abd Latiff
- Institute of Mathematical Sciences, Faculty of Science, Universiti Malaya, Kuala Lumpur, Malaysia
| | - Wan Ainun Mior Othman
- Institute of Mathematical Sciences, Faculty of Science, Universiti Malaya, Kuala Lumpur, Malaysia
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9
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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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10
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Synchronization in a Multiplex Network of Nonidentical Fractional-Order Neurons. FRACTAL AND FRACTIONAL 2022. [DOI: 10.3390/fractalfract6030169] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/17/2023]
Abstract
Fractional-order neuronal models that include memory effects can describe the rich dynamics of the firing of the neurons. This paper studies synchronization problems in a multiple network of Caputo–Fabrizio type fractional order neurons in which the orders of the derivatives in the layers are different. It is observed that the intralayer synchronization state occurs in weaker intralayer couplings when using nonidentical fractional-order derivatives rather than integer-order or identical fractional orders. Furthermore, the needed interlayer coupling strength for interlayer near synchronization decreases for lower fractional orders. The dynamics of the neurons in nonidentical layers are also considered. It is shown that in lower fractional orders, the neurons’ dynamics change to periodic when the near synchronization state occurs. Moreover, decreasing the derivative order leads to incrementing the frequency of the bursts in the synchronization manifold, which is in contrast to the behavior of the single neuron.
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11
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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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12
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Lyapunov Approach for Almost Periodicity in Impulsive Gene Regulatory Networks of Fractional Order with Time-Varying Delays. FRACTAL AND FRACTIONAL 2021. [DOI: 10.3390/fractalfract5040268] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
This paper investigates a class of fractional-order delayed impulsive gene regulatory networks (GRNs). The proposed model is an extension of some existing integer-order GRNs using fractional derivatives of Caputo type. The existence and uniqueness of an almost periodic state of the model are investigated and new criteria are established by the Lyapunov functions approach. The effects of time-varying delays and impulsive perturbations at fixed times on the almost periodicity are considered. In addition, sufficient conditions for the global Mittag–Leffler stability of the almost periodic solutions are proposed. To justify our findings a numerical example is also presented.
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13
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Stamov G, Stamova I, Spirova C. Impulsive Reaction-Diffusion Delayed Models in Biology: Integral Manifolds Approach. ENTROPY (BASEL, SWITZERLAND) 2021; 23:1631. [PMID: 34945937 PMCID: PMC8700440 DOI: 10.3390/e23121631] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Subscribe] [Scholar Register] [Received: 10/22/2021] [Revised: 11/27/2021] [Accepted: 11/30/2021] [Indexed: 11/16/2022]
Abstract
In this paper we study an impulsive delayed reaction-diffusion model applied in biology. The introduced model generalizes existing reaction-diffusion delayed epidemic models to the impulsive case. The integral manifolds notion has been introduced to the model under consideration. This notion extends the single state notion and has important applications in the study of multi-stable systems. By means of an extension of the Lyapunov method integral manifolds' existence, results are established. Based on the Lyapunov functions technique combined with a Poincarè-type inequality qualitative criteria related to boundedness, permanence, and stability of the integral manifolds are also presented. The application of the proposed impulsive control model is closely related to a most important problems in the mathematical biology-the problem of optimal control of epidemic models. The considered impulsive effects can be used by epidemiologists as a very effective therapy control strategy. In addition, since the integral manifolds approach is relevant in various contexts, our results can be applied in the qualitative investigations of many problems in the epidemiology of diverse interest.
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Affiliation(s)
- Gani Stamov
- Department of Mathematical Physics, Technical University of Sofia, 8800 Sliven, Bulgaria; (G.S.); (C.S.)
| | - Ivanka Stamova
- Department of Mathematics, University of Texas at San Antonio, San Antonio, TX 78249, USA
| | - Cvetelina Spirova
- Department of Mathematical Physics, Technical University of Sofia, 8800 Sliven, Bulgaria; (G.S.); (C.S.)
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14
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Xu Y, Sun F, Li W. Exponential synchronization of fractional-order multilayer coupled neural networks with reaction-diffusion terms via intermittent control. Neural Comput Appl 2021. [DOI: 10.1007/s00521-021-06214-0] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
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15
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Asymptotical stability of fractional neutral-type delayed neural networks with reaction-diffusion terms. Neurocomputing 2021. [DOI: 10.1016/j.neucom.2021.07.042] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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16
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Yang Y, Hu C, Yu J, Jiang H, Wen S. Synchronization of fractional-order spatiotemporal complex networks with boundary communication. Neurocomputing 2021. [DOI: 10.1016/j.neucom.2021.04.008] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
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17
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Zheng B, Hu C, Yu J, Jiang H. Synchronization analysis for delayed spatio-temporal neural networks with fractional-order. Neurocomputing 2021. [DOI: 10.1016/j.neucom.2021.01.128] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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18
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Yang S, Jiang H, Hu C, Yu J. Synchronization for fractional-order reaction–diffusion competitive neural networks with leakage and discrete delays. Neurocomputing 2021. [DOI: 10.1016/j.neucom.2021.01.009] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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19
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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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20
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Cao J, Stamov G, Stamova I, Simeonov S. Almost Periodicity in Impulsive Fractional-Order Reaction-Diffusion Neural Networks With Time-Varying Delays. IEEE TRANSACTIONS ON CYBERNETICS 2021; 51:151-161. [PMID: 32071019 DOI: 10.1109/tcyb.2020.2967625] [Citation(s) in RCA: 16] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
A neural-network model of fractional order with impulsive perturbations, time-varying delays, and reaction-diffusion terms is investigated in this article. The focus is on investigating qualitative properties of the states and developing new almost periodicity and stability criteria. The uncertain case is also considered. Examples are established and the effectiveness of the obtained criteria is demonstrated.
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21
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Zhang X, Ma Y. LMIs conditions to robust pinning synchronization of uncertain fractional-order neural networks with discontinuous activations. Soft comput 2020. [DOI: 10.1007/s00500-020-05315-7] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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22
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Liu XZ, Li ZT, Wu KN. Boundary Mittag-Leffler stabilization of fractional reaction-diffusion cellular neural networks. Neural Netw 2020; 132:269-280. [PMID: 32949988 DOI: 10.1016/j.neunet.2020.09.009] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2020] [Revised: 08/08/2020] [Accepted: 09/10/2020] [Indexed: 11/16/2022]
Abstract
Mittag-Leffler stabilization is studied for fractional reaction-diffusion cellular neural networks (FRDCNNs) in this paper. Different from previous literature, the FRDCNNs in this paper are high-dimensional systems, and boundary control and observed-based boundary control are both used to make FRDCNNs achieve Mittag-Leffler stability. First, a state-dependent boundary controller is designed when system states are available. By employing the spatial integral functional method and some inequalities, a criterion ensuring Mittag-Leffler stability of FRDCNNs is presented. Then, when the information of system states is not fully accessible, an observer is presented to estimate the system states based on boundary output and an observer-based boundary controller is provided aiming to stabilize the considered FRDCNNs. Furthermore, a robust observer-based boundary controller is proposed to ensure the Mittag-Leffler stability for FRDCNNs with uncertainties. Examples are given to illustrate the effectiveness of obtained theoretical results.
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Affiliation(s)
- Xiao-Zhen Liu
- Department of Mathematics, Harbin Institute of Technology, Weihai, 264209, China.
| | - Ze-Tao Li
- Department of Mathematics, Harbin Institute of Technology, Weihai, 264209, China.
| | - Kai-Ning Wu
- Department of Mathematics, Harbin Institute of Technology, Weihai, 264209, China.
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23
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Tuladhar R, Santamaria F, Stamova I. Fractional Lotka-Volterra-Type Cooperation Models: Impulsive Control on Their Stability Behavior. ENTROPY (BASEL, SWITZERLAND) 2020; 22:E970. [PMID: 33286739 PMCID: PMC7597273 DOI: 10.3390/e22090970] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 08/01/2020] [Revised: 08/26/2020] [Accepted: 08/27/2020] [Indexed: 11/29/2022]
Abstract
We present a biological fractional n-species delayed cooperation model of Lotka-Volterra type. The considered fractional derivatives are in the Caputo sense. Impulsive control strategies are applied for several stability properties of the states, namely Mittag-Leffler stability, practical stability and stability with respect to sets. The proposed results extend the existing stability results for integer-order n-species delayed Lotka-Volterra cooperation models to the fractional-order case under impulsive control.
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Affiliation(s)
- Rohisha Tuladhar
- Department of Biology, University of Texas at San Antonio, San Antonio, TX 78249, USA; (R.T.); (F.S.)
| | - Fidel Santamaria
- Department of Biology, University of Texas at San Antonio, San Antonio, TX 78249, USA; (R.T.); (F.S.)
| | - Ivanka Stamova
- Department of Mathematics, University of Texas at San Antonio, San Antonio, TX 78249, USA
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24
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Global Stability of Integral Manifolds for Reaction–Diffusion Delayed Neural Networks of Cohen–Grossberg-Type under Variable Impulsive Perturbations. MATHEMATICS 2020. [DOI: 10.3390/math8071082] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
The present paper introduces the concept of integral manifolds for a class of delayed impulsive neural networks of Cohen–Grossberg-type with reaction–diffusion terms. We establish new existence and boundedness results for general types of integral manifolds with respect to the system under consideration. Based on the Lyapunov functions technique and Poincarѐ-type inequality some new global stability criteria are also proposed in our research. In addition, we consider the case when the impulsive jumps are not realized at fixed instants. Instead, we investigate a system under variable impulsive perturbations. Finally, examples are given to demonstrate the efficiency and applicability of the obtained results.
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25
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Zhang H, Ding Z, Zeng Z. Adaptive tracking synchronization for coupled reaction–diffusion neural networks with parameter mismatches. Neural Netw 2020; 124:146-157. [DOI: 10.1016/j.neunet.2019.12.025] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2019] [Revised: 10/30/2019] [Accepted: 12/23/2019] [Indexed: 10/25/2022]
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26
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Lv Y, Hu C, Yu J, Jiang H, Huang T. Edge-Based Fractional-Order Adaptive Strategies for Synchronization of Fractional-Order Coupled Networks With Reaction-Diffusion Terms. IEEE TRANSACTIONS ON CYBERNETICS 2020; 50:1582-1594. [PMID: 30507521 DOI: 10.1109/tcyb.2018.2879935] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
In this paper, spatial diffusions are introduced to fractional-order coupled networks and the problem of synchronization is investigated for fractional-order coupled neural networks with reaction-diffusion terms. First, a new fractional-order inequality is established based on the Caputo partial fractional derivative. To realize asymptotical synchronization, two types of adaptive coupling weights are considered, namely: 1) coupling weights only related to time and 2) coupling weights dependent on both time and space. For each type of coupling weights, based on local information of the node's dynamics, an edge-based fractional-order adaptive law and an edge-based fractional-order pinning adaptive scheme are proposed. Furthermore, some new analytical tools, including the method of contradiction, L'Hopital rule, and Barbalat lemma are developed to establish adaptive synchronization criteria of the addressed networks. Finally, an example with numerical simulations is provided to illustrate the validity and effectiveness of the theoretical results.
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Stamov G, Stamova I, Martynyuk A, Stamov T. Design and Practical Stability of a New Class of Impulsive Fractional-Like Neural Networks. ENTROPY (BASEL, SWITZERLAND) 2020; 22:E337. [PMID: 33286111 PMCID: PMC7516808 DOI: 10.3390/e22030337] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/24/2020] [Revised: 03/11/2020] [Accepted: 03/13/2020] [Indexed: 11/17/2022]
Abstract
In this paper, a new class of impulsive neural networks with fractional-like derivatives is defined, and the practical stability properties of the solutions are investigated. The stability analysis exploits a new type of Lyapunov-like functions and their derivatives. Furthermore, the obtained results are applied to a bidirectional associative memory (BAM) neural network model with fractional-like derivatives. Some new results for the introduced neural network models with uncertain values of the parameters are also obtained.
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Affiliation(s)
- Gani Stamov
- Department of Mathematics, Technical University of Sofia, 8800 Sliven, Bulgaria
| | - Ivanka Stamova
- Department of Mathematics, University of Texas at San Antonio, San Antonio, TX 78249, USA
| | - Anatoliy Martynyuk
- S.P. Timoshenko Institute of Mechanics, NAS of Ukraine, 03057 Kiev-57, Ukraine
| | - Trayan Stamov
- Department of Machine Elements and Non-metallic Constructions, Technical University of Sofia, Sofia 1000, Bulgaria
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28
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Wang S, Guo Z, Wen S, Huang T. Global synchronization of coupled delayed memristive reaction–diffusion neural networks. Neural Netw 2020; 123:362-371. [DOI: 10.1016/j.neunet.2019.12.016] [Citation(s) in RCA: 17] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/06/2019] [Revised: 11/18/2019] [Accepted: 12/14/2019] [Indexed: 11/16/2022]
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Chen WH, Deng X, Lu X. Impulsive synchronization of two coupled delayed reaction–diffusion neural networks using time-varying impulsive gains. Neurocomputing 2020. [DOI: 10.1016/j.neucom.2019.08.098] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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Lu B, Jiang H, Hu C, Abdurahman A. Spacial sampled-data control for H ∞ output synchronization of directed coupled reaction-diffusion neural networks with mixed delays. Neural Netw 2020; 123:429-440. [PMID: 31954263 DOI: 10.1016/j.neunet.2019.12.026] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/23/2019] [Revised: 12/18/2019] [Accepted: 12/23/2019] [Indexed: 11/19/2022]
Abstract
This work investigates the H∞ output synchronization (HOS) of the directed coupled reaction-diffusion (R-D) neural networks (NNs) with mixed delays. Firstly, a model of the directed state coupled R-D NNs is introduced, which not only contains some discrete and distributed time delays, but also obeys a mixed Dirichlet-Neumann boundary condition. Secondly, a spacial sampled-data controller is proposed to achieve the HOS of the considered networks. This type of controller can reduce the update rate in the process of control by measuring the state of networks at some fixed sampling points in the space region. Moreover, some criteria for the HOS are established by designing an appropriate Lyapunov functional, and some quantitative relations between diffusion coefficients, mixed delays, coupling strength and control parameters are given accurately by these criteria. Thirdly, the case of directed spatial diffusion coupled networks is also studied and, the following finding is obtained: the spatial diffusion coupling can suppress the HOS while the state coupling can promote it. Finally, one example is simulated as the verification of the theoretical results.
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Affiliation(s)
- Binglong Lu
- College of Mathematics and System Science, Xinjiang University, Urumqi 830046, People's Republic of China
| | - Haijun Jiang
- College of Mathematics and System Science, Xinjiang University, Urumqi 830046, People's Republic of China.
| | - Cheng Hu
- College of Mathematics and System Science, Xinjiang University, Urumqi 830046, People's Republic of China
| | - Abdujelil Abdurahman
- College of Mathematics and System Science, Xinjiang University, Urumqi 830046, People's Republic of China
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31
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Stability of Sets Criteria for Impulsive Cohen-Grossberg Delayed Neural Networks with Reaction-Diffusion Terms. MATHEMATICS 2019. [DOI: 10.3390/math8010027] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
The paper proposes an extension of stability analysis methods for a class of impulsive reaction-diffusion Cohen-Grossberg delayed neural networks by addressing a challenge namely stability of sets. Such extended concept is of considerable interest to numerous systems capable of approaching not only one equilibrium state. Results on uniform global asymptotic stability and uniform global exponential stability with respect to sets for the model under consideration are established. The main tools are expansions of the Lyapunov method and the comparison principle. In addition, the obtained results for the uncertain case contributed to the development of the stability theory of uncertain reaction-diffusion Cohen-Grossberg delayed neural networks and their applications. Moreover, examples are given to demonstrate the feasibility of our results.
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32
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Impulsive Delayed Lasota–Wazewska Fractional Models: Global Stability of Integral Manifolds. MATHEMATICS 2019. [DOI: 10.3390/math7111025] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
In this paper we deal with the problems of existence, boundedness and global stability of integral manifolds for impulsive Lasota–Wazewska equations of fractional order with time-varying delays and variable impulsive perturbations. The main results are obtained by employing the fractional Lyapunov method and comparison principle for impulsive fractional differential equations. With this research we generalize and improve some existing results on fractional-order models of cell production systems. These models and applied technique can be used in the investigation of integral manifolds in a wide range of biological and chemical processes.
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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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34
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Hu B, Guan ZH, Chen G, Lewis FL. Multistability of Delayed Hybrid Impulsive Neural Networks With Application to Associative Memories. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2019; 30:1537-1551. [PMID: 30296243 DOI: 10.1109/tnnls.2018.2870553] [Citation(s) in RCA: 17] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
The important topic of multistability of continuous-and discrete-time neural network (NN) models has been investigated rather extensively. Concerning the design of associative memories, multistability of delayed hybrid NNs is studied in this paper with an emphasis on the impulse effects. Arising from the spiking phenomenon in biological networks, impulsive NNs provide an efficient model for synaptic interconnections among neurons. Using state-space decomposition, the coexistence of multiple equilibria of hybrid impulsive NNs is analyzed. Multistability criteria are then established regrading delayed hybrid impulsive neurodynamics, for which both the impulse effects on the convergence rate and the basins of attraction of the equilibria are discussed. Illustrative examples are given to verify the theoretical results and demonstrate an application to the design of associative memories. It is shown by an experimental example that delayed hybrid impulsive NNs have the advantages of high storage capacity and high fault tolerance when used for associative memories.
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Han M, Zhang M, Qiu T, Xu M. UCFTS: A Unilateral Coupling Finite-Time Synchronization Scheme for Complex Networks. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2019; 30:255-268. [PMID: 29994272 DOI: 10.1109/tnnls.2018.2837148] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Improving universality and robustness of the control method is one of the most challenging problems in the field of complex networks (CNs) synchronization. In this paper, a special unilateral coupling finite-time synchronization (UCFTS) method for uncertain CNs is proposed for this challenging problem. Multiple influencing factors are considered, so that the proposed method can be applied to a variety of situations. First, two kinds of drive-response CNs with different sizes are introduced, each of which contains two types of nonidentical nodes and time-varying coupling delay. In addition, the node parameters and topological structure are unknown in drive network. Then, an effective UCFTS control technique is proposed to realize the synchronization of drive-response CNs and identify the unknown parameters and topological structure. Second, the UCFTS of uncertain CNs with four types of nonidentical nodes is further studied. Moreover, both the networks are of unknown parameters, time-varying coupling delay and uncertain topological structure. Through designing corresponding adaptive updating laws, the unknown parameters are estimated successfully and the weight of uncertain topology can be automatically adapted to the appropriate value with the proposed UCFTS. Finally, two experimental examples show the correctness of the proposed scheme. Furthermore, the method is compared with the other three synchronization methods, which shows that our method has a better control performance.
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36
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Liu W, Jiang M, Yan M. Stability analysis of memristor-based time-delay fractional-order neural networks. Neurocomputing 2019. [DOI: 10.1016/j.neucom.2018.09.073] [Citation(s) in RCA: 16] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
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37
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Liu Y, Wang Z, Zhou D. UKF-based remote state estimation for discrete artificial neural networks with communication bandwidth constraints. Neural Netw 2018; 108:393-398. [DOI: 10.1016/j.neunet.2018.08.015] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/17/2018] [Revised: 04/27/2018] [Accepted: 08/13/2018] [Indexed: 10/28/2022]
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38
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Global Mittag–Leffler projective synchronization of nonidentical fractional-order neural networks with delay via sliding mode control. Neurocomputing 2018. [DOI: 10.1016/j.neucom.2018.06.029] [Citation(s) in RCA: 37] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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