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Yang Z, Zhang Z, Wang X. New finite-time synchronization conditions of delayed multinonidentical coupled complex dynamical networks. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2023; 20:3047-3069. [PMID: 36899571 DOI: 10.3934/mbe.2023144] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/18/2023]
Abstract
In this article, we mainly focus on the finite-time synchronization of delayed multinonidentical coupled complex dynamical networks. By applying the Zero-point theorem, novel differential inequalities, and designing three novel controllers, we obtain three new criteria to assure the finite-time synchronization between the drive system and the response system. The inequalities occurred in this paper are absolutely different from those in other papers. And the controllers provided here are fully novel. We also illustrate the theoretical results through some examples.
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Affiliation(s)
- Zhen Yang
- School of Science, Hubei University of Technology, Wuhan 430068, China
| | - Zhengqiu Zhang
- School of Mathematics, Hunan University, Changsha 410082, China
| | - Xiaoli Wang
- School of Science, Henan University of Technology, Zhengzhou 450001, China
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2
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Finite-Time Synchronization for Delayed Inertial Neural Networks by the Approach of the Same Structural Functions. Neural Process Lett 2022. [DOI: 10.1007/s11063-022-11075-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
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3
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Sheng Y, Zeng Z, Huang T. Finite-Time Stabilization of Competitive Neural Networks With Time-Varying Delays. IEEE TRANSACTIONS ON CYBERNETICS 2022; 52:11325-11334. [PMID: 34133310 DOI: 10.1109/tcyb.2021.3082153] [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 investigates finite-time stabilization of competitive neural networks with discrete time-varying delays (DCNNs). By virtue of comparison strategies and inequality techniques, finite-time stabilization of the underlying DCNNs is analyzed by designing a discontinuous state feedback controller, which simplifies the controller design and proof processes of some existing results. Meanwhile, global exponential stabilization of the DCNNs is provided under a continuous state feedback controller. In addition, global exponential stability of the DCNNs is shown as an M-matrix, which contains some published outcomes as special cases. Finally, three examples are given to illuminate the validity of the theories.
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Feng L, Yu J, Hu C, Yang C, Jiang H. Nonseparation Method-Based Finite/Fixed-Time Synchronization of Fully Complex-Valued Discontinuous Neural Networks. IEEE TRANSACTIONS ON CYBERNETICS 2021; 51:3212-3223. [PMID: 32275633 DOI: 10.1109/tcyb.2020.2980684] [Citation(s) in RCA: 20] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
This article mainly focuses on the problem of synchronization in finite and fixed time for fully complex-variable delayed neural networks involving discontinuous activations and time-varying delays without dividing the original complex-variable neural networks into two subsystems in the real domain. To avoid the separation method, a complex-valued sign function is proposed and its properties are established. By means of the introduced sign function, two discontinuous control strategies are developed under the quadratic norm and a new norm based on absolute values of real and imaginary parts. By applying nonsmooth analysis and some novel inequality techniques in the complex field, several synchronization criteria and the estimates of the settling time are derived. In particular, under the new norm framework, a unified control strategy is designed and it is revealed that a parameter value in the controller completely decides the networks are synchronized whether in finite time or in fixed time. Finally, some numerical results for an example are provided to support the established theoretical results.
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Li N, Zheng WX. Bipartite Synchronization of Multiple Memristor-Based Neural Networks With Antagonistic Interactions. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2021; 32:1642-1653. [PMID: 32324576 DOI: 10.1109/tnnls.2020.2985860] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
In this article, by introducing a signed graph to describe the coopetition interactions among network nodes, the mathematical model of multiple memristor-based neural networks (MMNNs) with antagonistic interactions is established. Since the cooperative and competitive interactions coexist, the states of MMNNs cannot reach complete synchronization. Instead, they will reach the bipartite synchronization: all nodes' states will reach an identical absolute value but opposite sign. To reach bipartite synchronization, two kinds of the novel node- and edge-based adaptive strategies are proposed, respectively. First, based on the global information of the network nodes, a node-based adaptive control strategy is constructed to solve the bipartite synchronization problem of MMNNs. Secondly, a local edge-based adaptive algorithm is proposed, where the weight values of edges between two nodes will change according to the designed adaptive law. Finally, two simulation examples validate the effectiveness of the proposed adaptive controllers and bipartite synchronization criteria.
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Wang JL, Qiu SH, Chen WZ, Wu HN, Huang T. Recent Advances on Dynamical Behaviors of Coupled Neural Networks With and Without Reaction-Diffusion Terms. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2020; 31:5231-5244. [PMID: 32175875 DOI: 10.1109/tnnls.2020.2964843] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Recently, the dynamical behaviors of coupled neural networks (CNNs) with and without reaction-diffusion terms have been widely researched due to their successful applications in different fields. This article introduces some important and interesting results on this topic. First, synchronization, passivity, and stability analysis results for various CNNs with and without reaction-diffusion terms are summarized, including the results for impulsive, time-varying, time-invariant, uncertain, fuzzy, and stochastic network models. In addition, some control methods, such as sampled-data control, pinning control, impulsive control, state feedback control, and adaptive control, have been used to realize the desired dynamical behaviors in CNNs with and without reaction-diffusion terms. In this article, these methods are summarized. Finally, some challenging and interesting problems deserving of further investigation are discussed.
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Gan Y, Liu C, Peng H, Liu F, Rao H. Anti-synchronization for periodic BAM neural networks with Markov scheduling protocol. Neurocomputing 2020. [DOI: 10.1016/j.neucom.2020.08.015] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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Lu W, Liu X, Chen T. Adaptive algorithms for synchronization, consensus of multi-agents and anti-synchronization of direct complex networks. Neurocomputing 2020. [DOI: 10.1016/j.neucom.2020.07.095] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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9
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Finite Time Anti-synchronization of Quaternion-Valued Neural Networks with Asynchronous Time-Varying Delays. Neural Process Lett 2020. [DOI: 10.1007/s11063-020-10348-y] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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Sheng Y, Lewis FL, Zeng Z, Huang T. Lagrange Stability and Finite-Time Stabilization of Fuzzy Memristive Neural Networks With Hybrid Time-Varying Delays. IEEE TRANSACTIONS ON CYBERNETICS 2020; 50:2959-2970. [PMID: 31059467 DOI: 10.1109/tcyb.2019.2912890] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
This paper focuses on Lagrange exponential stability and finite-time stabilization of Takagi-Sugeno (T-S) fuzzy memristive neural networks with discrete and distributed time-varying delays (DFMNNs). By resorting to theories of differential inclusions and the comparison strategy, an algebraic condition is developed to confirm Lagrange exponential stability of the underlying DFMNNs in Filippov's sense, and the exponentially attractive set is estimated. When external input is not considered, global exponential stability of DFMNNs is derived directly, which includes some existing ones as special cases. Furthermore, finite-time stabilization of the addressed DFMNNs is analyzed by exploiting inequality techniques and the comparison approach via designing a nonlinear state feedback controller. The boundedness assumption of activation functions is removed herein. Finally, two simulations are presented to demonstrate the validness of the outcomes, and an application is performed in pseudorandom number generation.
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Anti-synchronization of a Class Of Fuzzy Memristive Competitive Neural Networks with Different Time Scales. Neural Process Lett 2020. [DOI: 10.1007/s11063-020-10269-w] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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12
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Finite time anti-synchronization of complex-valued neural networks with bounded asynchronous time-varying delays. Neurocomputing 2020. [DOI: 10.1016/j.neucom.2020.01.035] [Citation(s) in RCA: 20] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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Shi Y, Cao J. Finite-time synchronization of memristive Cohen–Grossberg neural networks with time delays. Neurocomputing 2020. [DOI: 10.1016/j.neucom.2019.10.036] [Citation(s) in RCA: 20] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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Wan P, Sun D, Zhao M. Finite-time and fixed-time anti-synchronization of Markovian neural networks with stochastic disturbances via switching control. Neural Netw 2019; 123:1-11. [PMID: 31812925 DOI: 10.1016/j.neunet.2019.11.012] [Citation(s) in RCA: 20] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/03/2019] [Revised: 10/28/2019] [Accepted: 11/14/2019] [Indexed: 11/26/2022]
Abstract
This paper proposes a unified theoretical framework to study the problem of finite/fixed-time drive-response anti-synchronization for a class of Markovian stochastic neural networks. State feedback switching controllers without the sign function are designed to achieve the finite/fixed-time anti-synchronization of the addressed systems. Compared with the existing synchronization criteria, our results indicate that the controllers via the switching control without the sign function are given with less conservativeness, and the controllers without any sign function can deal with the chattering problem. By employing Lyapunov functional method and properties of the Weiner process, several finite/fixed-time synchronization criteria are presented and the corresponding settling times are calculated as well. Finally, three numerical examples are provided to illustrate the effectiveness of the theoretical results.
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Affiliation(s)
- Peng Wan
- Key Laboratory of Dependable Service Computing in Cyber Physical Society of Ministry of Education, Chongqing University, Chongqing 400044, China; School of Automation, Chongqing University, Chongqing 400044, China
| | - Dihua Sun
- Key Laboratory of Dependable Service Computing in Cyber Physical Society of Ministry of Education, Chongqing University, Chongqing 400044, China; School of Automation, Chongqing University, Chongqing 400044, China.
| | - Min Zhao
- Key Laboratory of Dependable Service Computing in Cyber Physical Society of Ministry of Education, Chongqing University, Chongqing 400044, China; School of Automation, Chongqing University, Chongqing 400044, China
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Zhang X, Niu P, Hu X, Ma Y, Li G. Global quasi-synchronization and global anti-synchronization of delayed neural networks with discontinuous activations via non-fragile control strategy. Neurocomputing 2019. [DOI: 10.1016/j.neucom.2019.07.041] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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Zhang Z, Zheng T, Yu S. Finite-time anti-synchronization of neural networks with time-varying delays via inequality skills. Neurocomputing 2019. [DOI: 10.1016/j.neucom.2019.05.012] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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Multi-Switching Combination Anti-synchronization of Unknown Hyperchaotic Systems. ARABIAN JOURNAL FOR SCIENCE AND ENGINEERING 2019. [DOI: 10.1007/s13369-019-03824-8] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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18
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Wang L, Chen T. Finite-time and fixed-time anti-synchronization of neural networks with time-varying delays. Neurocomputing 2019. [DOI: 10.1016/j.neucom.2018.10.057] [Citation(s) in RCA: 20] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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Liu Y, Liu X, Jing Y. Adaptive neural networks finite-time tracking control for non-strict feedback systems via prescribed performance. Inf Sci (N Y) 2018. [DOI: 10.1016/j.ins.2018.08.029] [Citation(s) in RCA: 86] [Impact Index Per Article: 14.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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