1
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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] [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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Wang J, Zhu S, Mu C, Liu X, Wen S. Unified analysis on multistablity of fraction-order multidimensional-valued memristive neural networks. Neural Netw 2024; 179:106498. [PMID: 38986183 DOI: 10.1016/j.neunet.2024.106498] [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: 02/05/2024] [Revised: 04/29/2024] [Accepted: 06/26/2024] [Indexed: 07/12/2024]
Abstract
This article provides a unified analysis of the multistability of fraction-order multidimensional-valued memristive neural networks (FOMVMNNs) with unbounded time-varying delays. Firstly, based on the knowledge of fractional differentiation and memristors, a unified model is established. This model is a unified form of real-valued, complex-valued, and quaternion-valued systems. Then, based on a unified method, the number of equilibrium points for FOMVMNNs is discussed. The sufficient conditions for determining the number of equilibrium points have been obtained. By using 1-norm to construct Lyapunov functions, the unified criteria for multistability of FOMVMNNs are obtained, these criteria are less conservative and easier to verify. Moreover, the attraction basins of the stable equilibrium points are estimated. Finally, two numerical simulation examples are provided to verify the correctness of the results.
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Affiliation(s)
- Jiarui 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.
| | - Chaoxu Mu
- School of Electrical and Automation Engineering, Tianjin University, Tianjin, 300072, 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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3
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Lan J, Zhang X, Wang X. Global robust exponential stability of interval BAM neural networks with multiple time-varying delays: A direct method based on system solutions. ISA TRANSACTIONS 2024; 144:145-152. [PMID: 37951754 DOI: 10.1016/j.isatra.2023.11.001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/02/2023] [Revised: 10/31/2023] [Accepted: 11/01/2023] [Indexed: 11/14/2023]
Abstract
This paper analyzes global robust exponential stability of interval bidirectional associative memory (BAM) neural networks with multiple time-varying delays, proposes a direct method based on system solutions, and gives sufficient conditions under which interval BAM neural networks have a unique and globally robustly exponentially stable equilibrium point. This method not only avoids the difficult to set up any Lyapunov-Krasovskii functional, but also derives simpler global robust exponential stability criteria. Compared with the data from other literature, the robust exponential stability criteria obtained in this paper have been presented to have more merits theoretically and numerically.
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Affiliation(s)
- Jinbao Lan
- School of Mathematical Science, Heilongjiang University, Harbin, 150080, PR China.
| | - Xian Zhang
- School of Mathematical Science, Heilongjiang University, Harbin, 150080, PR China; Heilongjiang Provincial Key Laboratory of the Theory and Computation of Complex Systems, Heilongjiang University, Harbin, 150080, PR China.
| | - Xin Wang
- School of Mathematical Science, Heilongjiang University, Harbin, 150080, PR China; Heilongjiang Provincial Key Laboratory of the Theory and Computation of Complex Systems, Heilongjiang University, Harbin, 150080, PR China.
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4
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Meng X, Li Z, Cao J. Almost periodic quasi-projective synchronization of delayed fractional-order quaternion-valued neural networks. Neural Netw 2024; 169:92-107. [PMID: 37864999 DOI: 10.1016/j.neunet.2023.10.017] [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: 05/31/2023] [Revised: 09/03/2023] [Accepted: 10/11/2023] [Indexed: 10/23/2023]
Abstract
This paper examines the issue of almost periodic quasi-projective synchronization of delayed fractional-order quaternion-valued neural networks. First, using a direct method rather than decomposing the fractional quaternion-valued system into four equivalent fractional real-valued systems, using Banach's fixed point theorem, according to the basic properties of fractional calculus and some inequality methods, we obtain that there is a unique almost periodic solution for this class of neural network with some sufficient conditions. Next, by constructing a suitable Lyapunov functional, using the characteristic of the Mittag-Leffler function and the scaling idea of the inequality, the adequate conditions for the quasi-projective synchronization of the established model are derived, and the upper bound of the systematic error is estimated. Finally, further use Matlab is used to carry out two numerical simulations to prove the results of theoretical analysis.
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Affiliation(s)
- Xiaofang Meng
- School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan 650021, China
| | - Zhouhong Li
- School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan 650021, China; Department of Mathematics, Yuxi Normal University, Yuxi, Yunnan 653100, China.
| | - Jinde Cao
- School of Mathematics, Southeast University, Nanjing 210096, China; Yonsei Frontier Lab, Yonsei University, Seoul 03722, South Korea
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5
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Zhou Y, Lv W, Tao J, Xu Y, Huang T, Rutkowski L. Event-triggered impulsive quasi-synchronization for BAM neural networks with reliable redundant channel. Neural Netw 2024; 169:485-495. [PMID: 37939537 DOI: 10.1016/j.neunet.2023.10.045] [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: 04/17/2023] [Revised: 09/27/2023] [Accepted: 10/29/2023] [Indexed: 11/10/2023]
Abstract
This work addresses the quasi-synchronization of delay master-slave BAM neural networks. To improve the utilization of channel bandwidth, a dynamic event-triggered impulsive mechanism is employed, in which data is transmitted only when a preset event-triggered mechanism or a forced impulse interval is satisfied. In addition, to guarantee the reliability of information transmission, a reliable redundant channel for BAM neural networks is adopted, whose transmission scheduling strategy is designed on the basis of the packet dropouts rate of the main communication channels. Further, an algorithm is employed to reduce the quasi-synchronization range of the error systems and the controllers are obtained. At last, a simulation result is shown to illustrate the effectiveness of the presented strategy.
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Affiliation(s)
- Yumei Zhou
- Guangdong Provincial Key Laboratory of Intelligent Decision and Cooperative Control, School of Automation, Guangdong University of Technology, Guangzhou 510006, China.
| | - Weijun Lv
- Guangdong Provincial Key Laboratory of Intelligent Decision and Cooperative Control, School of Automation, Guangdong University of Technology, Guangzhou 510006, China.
| | - Jie Tao
- Guangdong Provincial Key Laboratory of Intelligent Decision and Cooperative Control, School of Automation, Guangdong University of Technology, Guangzhou 510006, China.
| | - Yong Xu
- Guangdong Provincial Key Laboratory of Intelligent Decision and Cooperative Control, School of Automation, Guangdong University of Technology, Guangzhou 510006, China.
| | - Tingwen Huang
- Science Program, Texas A & M University at Qatar, Doha 23874, Qatar.
| | - Leszek Rutkowski
- Systems Research Institute of the Polish Academy of Sciences, 01-447 Warsaw, Poland; Institute of Computer Science, AGH University of Science and Technology in Kraków, 30-059 Kraków, Poland; Information Technology Institute, University of Social Sciences, 90-113 Łódź, Poland.
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6
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Yang F, Wang W, Li L, Zheng M, Zhang Y, Liang Z. Finite-time parameter identification of fractional-order time-varying delay neural networks based on synchronization. CHAOS (WOODBURY, N.Y.) 2023; 33:033146. [PMID: 37003798 DOI: 10.1063/5.0137598] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/04/2022] [Accepted: 03/03/2023] [Indexed: 06/19/2023]
Abstract
We research the finite-time parameter identification of fractional-order time-varying delay neural networks (FTVDNNs) based on synchronization. First, based on the fractional-order Lyapunov stability theorem and feedback control idea, we construct a synchronous controller and some parameter update rules, which accomplish the synchronization of the drive-response FTVDNNs and complete the identification of uncertain parameters. Second, the theoretical analysis of the synchronization method is carried out, and the stable time is calculated. Finally, we give two examples for simulation verification. Our method can complete the synchronization of the FTVDNNs in finite time and identify uncertain parameters while synchronizing.
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Affiliation(s)
- Fan Yang
- School of Mathematics and Statistics, Shandong University of Technology, Zibo 255000, China
| | - Wen Wang
- School of Mathematics and Statistics, Shandong University of Technology, Zibo 255000, China
| | - Lixiang Li
- Information Security Center, State Key Laboratory of Networking and Switching Technology, and National Engineering Laboratory for Disaster Backup and Recovery, Beijing University of Posts and Telecommunications, Beijing 100086, China
| | - Mingwen Zheng
- School of Mathematics and Statistics, Shandong University of Technology, Zibo 255000, China
| | - Yanping Zhang
- School of Mathematics and Statistics, Shandong University of Technology, Zibo 255000, China
| | - Zhenying Liang
- School of Mathematics and Statistics, Shandong University of Technology, Zibo 255000, China
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7
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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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8
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Ramajayam S, Rajavel S, Samidurai R, Cao Y. Finite-Time Synchronization for T–S Fuzzy Complex-Valued Inertial Delayed Neural Networks Via Decomposition Approach. Neural Process Lett 2023. [DOI: 10.1007/s11063-022-11117-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023]
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9
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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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10
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Xiao J, Zhong S, Wen S. Unified Analysis on the Global Dissipativity and Stability of Fractional-Order Multidimension-Valued Memristive Neural Networks With Time Delay. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2022; 33:5656-5665. [PMID: 33950847 DOI: 10.1109/tnnls.2021.3071183] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
The unified criteria are analyzed on the global dissipativity and stability for the delayed fractional-order systems of multidimension-valued memristive neural networks (FSMVMNNs) in this article. First, based on the comprehensive knowledge about multidimensional algebra, fractional derivatives, and nonsmooth analysis, we establish the unified model for the studied FSMVMNNs in order to propose a more uniform method to analyze the dynamic behaviors of multidimensional neural networks. Then, by mainly applying the Lyapunov method, employing several new lemmas, and solving some mathematical difficulties, without any separation, we acquire the unified and concise criteria. The derived criteria have many advantages in a smaller calculation, lower conservatism, more diversity, and higher flexibility. Finally, we provide two numerical examples to express the availability and improvements of the theoretical results.
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11
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Mao X, Wang X, Qin H. Stability analysis of quaternion-valued BAM neural networks fractional-order model with impulses and proportional delays. Neurocomputing 2022. [DOI: 10.1016/j.neucom.2022.08.059] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/15/2022]
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12
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Synchronization analysis and parameters identification of uncertain delayed fractional-order BAM neural networks. Neural Comput Appl 2022. [DOI: 10.1007/s00521-022-07791-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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13
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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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14
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Extended analysis on the global Mittag-Leffler synchronization problem for fractional-order octonion-valued BAM neural networks. Neural Netw 2022; 154:491-507. [DOI: 10.1016/j.neunet.2022.07.031] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/03/2022] [Revised: 06/16/2022] [Accepted: 07/26/2022] [Indexed: 11/22/2022]
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15
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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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16
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Synchronization and state estimation for discrete-time coupled delayed complex-valued neural networks with random system parameters. Neural Netw 2022; 150:181-193. [DOI: 10.1016/j.neunet.2022.02.028] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/24/2021] [Revised: 01/07/2022] [Accepted: 02/28/2022] [Indexed: 11/21/2022]
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17
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Mittag–Leffler Synchronization of Caputo-Delayed Quaternion BAM Neural Networks via Adaptive and Linear Feedback Control Designs. ELECTRONICS 2022. [DOI: 10.3390/electronics11111746] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/07/2022]
Abstract
The Mittag–Leffler synchronization (MLS) issue for Caputo-delayed quaternion bidirectional associative memory neural networks (BAM-NNs) is studied in this paper. Firstly, a novel lemma is proved by the Laplace transform and inverse transform. Then, without decomposing a quaternion system into subsystems, the adaptive controller and the linear controller are designed to realize MLS. According to the proposed lemma, constructing two different Lyapunov functionals and applying the fractional Razumikhin theorem and inequality techniques, the sufficient criteria of MLS on fractional delayed quaternion BAM-NNs are derived. Finally, two numerical examples are given to illustrate the validity and practicability.
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18
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Finite-Time Synchronization Analysis for BAM Neural Networks with Time-Varying Delays by Applying the Maximum-Value Approach with New Inequalities. MATHEMATICS 2022. [DOI: 10.3390/math10050835] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/10/2022]
Abstract
In this paper, we consider the finite-time synchronization for drive-response BAM neural networks with time-varying delays. Instead of using the finite-time stability theorem and integral inequality method, by using the maximum-value method, two new criteria are obtained to ensure the finite-time synchronization for the considered drive-response systems. The inequalities in our paper, applied to obtaining the maximum-valued and designing the novel controllers, are different from those in existing papers.
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19
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Shan Y, She K, Zhong S, Cheng J, Yu Y, Deng H. Asynchronous H ∞ control of Markov jump discrete-time systems with incomplete transition probability and unreliable links. ISA TRANSACTIONS 2022; 122:218-231. [PMID: 33993995 DOI: 10.1016/j.isatra.2021.04.044] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/07/2020] [Revised: 04/29/2021] [Accepted: 04/29/2021] [Indexed: 06/12/2023]
Abstract
In this study, an asynchronous H∞ state feedback controller is devised for Markov jump discrete-time systems (MJDTSs) with time-varying delay. "Asynchronous" means that the system switching mode θk, the controller mode ϑk and the quantizer mode λk are different from each other. The first one is homogeneous and the last two are non-homogeneous. In particular, as a promotion of existing work, we firstly attempt to propose the transition probabilities (TPs) of the three Markov chains (MCs) are not completely known. In addition, the discrete time-varying delay and its infinitely distributed ones are considered. Moreover, according to the Lyapunov stability theory and stochastic process, it is established for the sufficient criterion to ensure the stochastic stability of resulting closed-loop MJDTSs with an H∞ attenuation performance index. The feasibility and effectiveness of the proposed method are validated by three examples.
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Affiliation(s)
- Yaonan Shan
- College of Mathematics and Information Science, Zhengzhou University of Light Industry, Zhengzhou, 450002, PR China.
| | - Kun She
- School of Information and Software Engineering, University of Electronic Science and Technology of China, Chengdu, 611731, PR China
| | - Shouming Zhong
- School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, 611731, PR China
| | - Jun Cheng
- College of Mathematics and Statistics, Guangxi Normal University, Guilin, 541006, PR China; School of Information Science and Engineering, Chengdu University, Chengdu, 610106, PR China
| | - Yongbin Yu
- School of Information and Software Engineering, University of Electronic Science and Technology of China, Chengdu, 611731, PR China
| | - Hongyao Deng
- College of Computer Engineering and Information, Yangtze Normal University, Chongqing, 408000, PR China
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20
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Yan H, Qiao Y, Duan L, Miao J. New inequalities to finite-time synchronization analysis of delayed fractional-order quaternion-valued neural networks. Neural Comput Appl 2022. [DOI: 10.1007/s00521-022-06976-1] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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21
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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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22
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Xiao J, Li Y, Wen S. Mittag-Leffler synchronization and stability analysis for neural networks in the fractional-order multi-dimension field. Knowl Based Syst 2021. [DOI: 10.1016/j.knosys.2021.107404] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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23
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Sarkar A, Khan MZ, Alahmadi AH. Neural weight coordination-based vector-valued neural network synchronization. Neurocomputing 2021. [DOI: 10.1016/j.neucom.2021.08.111] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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24
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Cao Y, Ramajayam S, Sriraman R, Samidurai R. Leakage delay on stabilization of finite-time complex-valued BAM neural network: Decomposition approach. Neurocomputing 2021. [DOI: 10.1016/j.neucom.2021.08.056] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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25
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Zhang L, Zhong J, Lu J. Intermittent control for finite-time synchronization of fractional-order complex networks. Neural Netw 2021; 144:11-20. [PMID: 34438324 DOI: 10.1016/j.neunet.2021.08.004] [Citation(s) in RCA: 30] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/02/2021] [Revised: 07/05/2021] [Accepted: 08/02/2021] [Indexed: 11/17/2022]
Abstract
This paper is concerned with the finite-time synchronization problem for fractional-order complex dynamical networks (FCDNs) with intermittent control. Using the definition of Caputo's fractional derivative and the properties of Beta function, the Caputo fractional-order derivative of the power function is evaluated. A general fractional-order intermittent differential inequality is obtained with fewer additional constraints. Then, the criteria are established for the finite-time convergence of FCDNs under intermittent feedback control, intermittent adaptive control and intermittent pinning control indicate that the setting time is related to order of FCDNs and initial conditions. Finally, these theoretical results are illustrated by numerical examples.
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Affiliation(s)
- Lingzhong Zhang
- School of Electrical Engineering and Automation, Changshu Institute of Technology, Changshu 215500, China
| | - Jie Zhong
- College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, China.
| | - Jianquan Lu
- School of Mathematics, Southeast University, Nanjing 210096, China
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26
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Multiple asymptotic stability of fractional-order quaternion-valued neural networks with time-varying delays. Neurocomputing 2021. [DOI: 10.1016/j.neucom.2021.03.079] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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27
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Xiao J, Cao J, Cheng J, Wen S, Zhang R, Zhong S. Novel Inequalities to Global Mittag-Leffler Synchronization and Stability Analysis of Fractional-Order Quaternion-Valued Neural Networks. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2021; 32:3700-3709. [PMID: 32997634 DOI: 10.1109/tnnls.2020.3015952] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
This article is concerned with the problem of the global Mittag-Leffler synchronization and stability for fractional-order quaternion-valued neural networks (FOQVNNs). The systems of FOQVNNs, which contain either general activation functions or linear threshold ones, are successfully established. Meanwhile, two distinct methods, such as separation and nonseparation, have been employed to solve the transformation of the studied systems of FOQVNNs, which dissatisfy the commutativity of quaternion multiplication. Moreover, two novel inequalities are deduced based on the general parameters. Compared with the existing inequalities, the new inequalities have their unique superiorities because they can make full use of the additional parameters. Due to the Lyapunov theory, two novel Lyapunov-Krasovskii functionals (LKFs) can be easily constructed. The novelty of LKFs comes from a wider range of parameters, which can be involved in the construction of LKFs. Furthermore, mainly based on the new inequalities and LKFs, more multiple and more flexible criteria are efficiently obtained for the discussed problem. Finally, four numerical examples are given to demonstrate the related effectiveness and availability of the derived criteria.
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Cheng Y, Hu T, Li Y, Zhang X, Zhong S. Delay-dependent consensus criteria for fractional-order Takagi-Sugeno fuzzy multi-agent systems with time delay. Inf Sci (N Y) 2021. [DOI: 10.1016/j.ins.2021.01.074] [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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29
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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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30
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Yan M, Jian J, Zheng S. Passivity analysis for uncertain BAM inertial neural networks with time-varying delays. Neurocomputing 2021. [DOI: 10.1016/j.neucom.2020.12.073] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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31
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You X, Dian S, Guo R, Li S. Exponential stability analysis for discrete-time quaternion-valued neural networks with leakage delay and discrete time-varying delays. Neurocomputing 2021. [DOI: 10.1016/j.neucom.2020.12.021] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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32
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Song Q, Chen Y, Zhao Z, Liu Y, Alsaadi FE. Robust stability of fractional-order quaternion-valued neural networks with neutral delays and parameter uncertainties. Neurocomputing 2021. [DOI: 10.1016/j.neucom.2020.08.059] [Citation(s) in RCA: 47] [Impact Index Per Article: 15.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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33
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A further study on bifurcation for fractional order BAM neural networks with multiple delays. Neurocomputing 2020. [DOI: 10.1016/j.neucom.2020.08.047] [Citation(s) in RCA: 27] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Xiao J, Zhong S, Wen S. Improved approach to the problem of the global Mittag-Leffler synchronization for fractional-order multidimension-valued BAM neural networks based on new inequalities. Neural Netw 2020; 133:87-100. [PMID: 33152567 DOI: 10.1016/j.neunet.2020.10.008] [Citation(s) in RCA: 17] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/18/2020] [Revised: 09/13/2020] [Accepted: 10/15/2020] [Indexed: 11/17/2022]
Abstract
This paper studies the problem of the global Mittag-Leffler synchronization for fractional-order multidimension-valued BAM neural networks (FOMVBAMNNs) with general activation functions (AFs). First, the unified model is established for the researched systems of FOMVBAMNNs which can be turned into the corresponding multidimension-valued systems as long as the state variables, the connection weights and the AFs of the neural networks are valued to be real, complex, or quaternion. Then, without any decomposition, the criteria in unified form are derived by constructing the new Lyapunov-Krasovskii functionals (LKFs) in vector form, combining two new inequalities and considering the easy controllers. It is worth mentioning that the obtained criteria have many advantages in higher flexibility, more diversity, smaller computation, and lower conservatism. Finally, a simulation example is provided to illustrate the availability and improvements of the acquired results.
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Affiliation(s)
- Jianying Xiao
- School of Sciences, Southwest Petroleum University, Chengdu, 610050, PR China.
| | - Shouming Zhong
- School of Mathematical Sciences, University of Electronic Science and Technology, Chengdu, 611731, PR China.
| | - Shiping Wen
- Centre for Artificial Intelligence, Faculty of Engineering Information Technology, University of Technology Sydney, Ultimo, NSW, 2007, Australia.
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Xu X, Xu Q, Yang J, Xue H, Xu Y. Further research on exponential stability for quaternion-valued neural networks with mixed delays. Neurocomputing 2020. [DOI: 10.1016/j.neucom.2020.03.004] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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36
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Novel methods to finite-time Mittag-Leffler synchronization problem of fractional-order quaternion-valued neural networks. Inf Sci (N Y) 2020. [DOI: 10.1016/j.ins.2020.03.101] [Citation(s) in RCA: 54] [Impact Index Per Article: 13.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
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37
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Faydasicok O. A new Lyapunov functional for stability analysis of neutral-type Hopfield neural networks with multiple delays. Neural Netw 2020; 129:288-297. [PMID: 32574975 DOI: 10.1016/j.neunet.2020.06.013] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/30/2020] [Revised: 05/30/2020] [Accepted: 06/11/2020] [Indexed: 10/24/2022]
Abstract
This research paper conducts an investigation into the stability issue for a more general class of neutral-type Hopfield neural networks that involves multiple time delays in the states of neurons and multiple neutral delays in the time derivatives of the states of neurons. By constructing a new proper Lyapunov functional, an alternative easily verifiable algebraic criterion for global asymptotic stability of this type of Hopfield neural systems is derived. This new stability condition is entirely independent of time and neutral delays. Two instructive examples are employed to indicate that the result obtained in this paper reveals a new set of sufficient stability criteria when it is compared with the previously reported stability results. Therefore, the proposed stability result enlarges the application domain of Hopfield neural systems of neutral types.
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Affiliation(s)
- Ozlem Faydasicok
- Department of Mathematics, Faculty of Science, Istanbul University, Vezneciler, Istanbul, Turkey.
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Stochastic Memristive Quaternion-Valued Neural Networks with Time Delays: An Analysis on Mean Square Exponential Input-to-State Stability. MATHEMATICS 2020. [DOI: 10.3390/math8050815] [Citation(s) in RCA: 29] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
In this paper, we study the mean-square exponential input-to-state stability (exp-ISS) problem for a new class of neural network (NN) models, i.e., continuous-time stochastic memristive quaternion-valued neural networks (SMQVNNs) with time delays. Firstly, in order to overcome the difficulties posed by non-commutative quaternion multiplication, we decompose the original SMQVNNs into four real-valued models. Secondly, by constructing suitable Lyapunov functional and applying It o ^ ’s formula, Dynkin’s formula as well as inequity techniques, we prove that the considered system model is mean-square exp-ISS. In comparison with the conventional research on stability, we derive a new mean-square exp-ISS criterion for SMQVNNs. The results obtained in this paper are the general case of previously known results in complex and real fields. Finally, a numerical example has been provided to show the effectiveness of the obtained theoretical results.
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Global Stability Analysis of Fractional-Order Quaternion-Valued Bidirectional Associative Memory Neural Networks. MATHEMATICS 2020. [DOI: 10.3390/math8050801] [Citation(s) in RCA: 40] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
We study the global asymptotic stability problem with respect to the fractional-order quaternion-valued bidirectional associative memory neural network (FQVBAMNN) models in this paper. Whether the real and imaginary parts of quaternion-valued activation functions are expressed implicitly or explicitly, they are considered to meet the global Lipschitz condition in the quaternion field. New sufficient conditions are derived by applying the principle of homeomorphism, Lyapunov fractional-order method and linear matrix inequality (LMI) approach for the two cases of activation functions. The results confirm the existence, uniqueness and global asymptotic stability of the system’s equilibrium point. Finally, two numerical examples with their simulation results are provided to show the effectiveness of the obtained results.
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40
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Global Mittag–Leffler Stability and Stabilization Analysis of Fractional-Order Quaternion-Valued Memristive Neural Networks. MATHEMATICS 2020. [DOI: 10.3390/math8030422] [Citation(s) in RCA: 42] [Impact Index Per Article: 10.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
This paper studies the global Mittag–Leffler stability and stabilization analysis of fractional-order quaternion-valued memristive neural networks (FOQVMNNs). The state feedback stabilizing control law is designed in order to stabilize the considered problem. Based on the non-commutativity of quaternion multiplication, the original fractional-order quaternion-valued systems is divided into four fractional-order real-valued systems. By using the method of Lyapunov fractional-order derivative, fractional-order differential inclusions, set-valued maps, several global Mittag–Leffler stability and stabilization conditions of considered FOQVMNNs are established. Two numerical examples are provided to illustrate the usefulness of our analytical results.
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