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Zhu S, Zhou J, Zhu Q, Li N, Lu JA. Adaptive Exponential Synchronization of Complex Networks With Nondifferentiable Time-Varying Delay. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2023; 34:8124-8130. [PMID: 35139027 DOI: 10.1109/tnnls.2022.3145843] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
In recent years, the adaptive exponential synchronization (AES) problem of delayed complex networks has been extensively studied. Existing results rely heavily on assuming the differentiability of the time-varying delay, which is not easy to verify in reality. Dealing with nondifferentiable delay in the field of AES is still a challenging problem. In this brief, the AES problem of complex networks with general time-varying delay is addressed, especially when the delay is nondifferentiable. A delay differential inequality is proposed to deal with the exponential stability of delayed nonlinear systems, which is more general than the widely used Halanay inequality. Next, the boundedness of the adaptive control gain is theoretically proved, which is neglected in much of the literature. Then, the AES criteria for networks with general delay are established for the first time by using the proposed inequality and the boundedness of the control gain. Finally, an example is given to demonstrate the effectiveness of the theoretical results.
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Tang R, Miao Z, Jiang S, Chen X, Wang H, Wang W. Interlayer Link Prediction in Multiplex Social Networks Based on Multiple Types of Consistency Between Embedding Vectors. IEEE TRANSACTIONS ON CYBERNETICS 2023; 53:2426-2439. [PMID: 34735350 DOI: 10.1109/tcyb.2021.3120134] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
Online users are typically active on multiple social media networks (SMNs), which constitute a multiplex social network. With improvements in cybersecurity awareness, users increasingly choose different usernames and provide different profiles on different SMNs. Thus, it is becoming increasingly challenging to determine whether given accounts on different SMNs belong to the same user; this can be expressed as an interlayer link prediction problem in a multiplex network. To address the challenge of predicting interlayer links, feature or structure information is leveraged. Existing methods that use network embedding techniques to address this problem focus on learning a mapping function to unify all nodes into a common latent representation space for prediction; positional relationships between unmatched nodes and their common matched neighbors (CMNs) are not utilized. Furthermore, the layers are often modeled as unweighted graphs, ignoring the strengths of the relationships between nodes. To address these limitations, we propose a framework based on multiple types of consistency between embedding vectors (MulCEVs). In MulCEV, the traditional embedding-based method is applied to obtain the degree of consistency between the vectors representing the unmatched nodes, and a proposed distance consistency index based on the positions of nodes in each latent space provides additional clues for prediction. By associating these two types of consistency, the effective information in the latent spaces is fully utilized. In addition, MulCEV models the layers as weighted graphs to obtain representation. In this way, the higher the strength of the relationship between nodes, the more similar their embedding vectors in the latent representation space will be. The results of our experiments on several real-world and synthetic datasets demonstrate that the proposed MulCEV framework markedly outperforms current embedding-based methods, especially when the number of training iterations is small.
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Wang L, Bian Y, Guo Z, Hu M. Lag H∞ synchronization in coupled reaction–diffusion neural networks with multiple state or derivative couplings. Neural Netw 2022; 156:179-192. [DOI: 10.1016/j.neunet.2022.09.030] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/01/2022] [Revised: 08/12/2022] [Accepted: 09/26/2022] [Indexed: 11/07/2022]
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Bipartite leader–follower consensus for nonlinear signed networks with impulsive control. Neural Comput Appl 2022. [DOI: 10.1007/s00521-022-07860-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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Luo T, Wang Q, Jia Q, Xu Y. Asymptotic and finite-time synchronization of fractional-order multiplex networks with time delays by adaptive and impulsive control. Neurocomputing 2022. [DOI: 10.1016/j.neucom.2021.12.087] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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Wang JL, Zhao LH, Wu HN, Huang T. Finite-Time Passivity and Synchronization of Multi-Weighted Complex Dynamical Networks Under PD Control. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2022; PP:507-518. [PMID: 35635821 DOI: 10.1109/tnnls.2022.3175747] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
This article focuses on finite-time passivity (FTP) and finite-time synchronization (FTS) for complex dynamical networks with multiple state/derivative couplings based on the proportional-derivative (PD) control method. Several criteria of FTP for complex dynamical networks with multiple state couplings (CDNMSCs) are formulated by utilizing the PD controller and constructing an appropriate Lyapunov function. Furthermore, FTP is further used to investigate the FTS in CDNMSCs under the PD controller. In addition, the FTP and FTS for complex dynamical networks with multiple derivative couplings (CDNMDCs) are also studied by exploiting the PD control method and some inequality techniques. Finally, two numerical examples are worked out to demonstrate the validity of the presented PD controllers.
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Liu H, Li J, Li Z, Zeng Z, Lu J. Intralayer Synchronization of Multiplex Dynamical Networks via Pinning Impulsive Control. IEEE TRANSACTIONS ON CYBERNETICS 2022; 52:2110-2122. [PMID: 32697736 DOI: 10.1109/tcyb.2020.3006032] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
These days, the synchronization of multiplex networks is an emerging and important research topic. Grounded framework and theory about synchronization and control on multiplex networks are yet to come. This article studies the intralayer synchronization on a multiplex network (i.e., a set of networks connected through interlayer edges), via the pinning impulsive control method. The topologies of different layers are independent of each other, and the individual dynamics of nodes in different layers are different as well. Supra-Laplacian matrices are adopted to represent the topological structures of multiplex networks. Two cases are considered according to impulsive sequences of multiplex networks: 1) pinning controllers are applied to all the layers simultaneously at the instants of a common impulse sequence and 2) pinning controllers are applied to each layer at the instants of distinct impulse sequences. Using the Lyapunov stability theory and the impulsive control theory, several intralayer synchronization criteria for multiplex networks are obtained, in terms of the supra-Laplacian matrix of network topology, self-dynamics of nodes, impulsive intervals, and the pinning control effect. Furthermore, the algorithms for implementing pinning schemes at every impulsive instant are proposed to support the obtained criteria. Finally, numerical examples are presented to demonstrate the effectiveness and correctness of the proposed schemes.
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Luo M, Cheng J, Shi K, Hu C, Lan J. Security synchronization protocol for IT2 stochastic fuzzy multiplex complex networks via fuzzy hybrid control. ISA TRANSACTIONS 2021; 118:94-105. [PMID: 33612274 DOI: 10.1016/j.isatra.2021.02.010] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/19/2020] [Revised: 01/20/2021] [Accepted: 02/08/2021] [Indexed: 06/12/2023]
Abstract
An issue regarding security synchronization is addressed for a class of interval type-2 (IT2) fuzzy stochastic multiplex complex networks with fuzzy hybrid control under deception attacks. Firstly, some complicated facts are considered in a unified network framework, such as multiplex, multiple delays, and stochastic disturbances, etc. In particular, different from the traditional hypothesis, the uncertainty is taken into consideration for the membership functions and along with the strategy of upper and lower bound and the correlative tradeoff functions to overcome this uncertainty. Secondly, malicious data are injected into channels between sensor and controller that may lead to undesired system performance. Then, based on Lyapunov stability theory and comparison principle, a novel IT2 fuzzy hybrid controller, containing a state feedback controller and a network-based impulsive controller, is designed to ensure a mean-square bounded synchronization so that the error states can converge below error thresholds. Finally, impulsive effects including both positive and negative roles are considered simultaneously in the security synchronization strategy, and the feasibility of the designed scenario is demonstrated by two numerical examples.
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Affiliation(s)
- Mengzhuo Luo
- College of Science, Guilin University of Technology, Guilin, Guangxi, 541004, PR China; Guangxi Key Laboratory of Spatial Information and Geomatics, Guilin, Guangxi, 541004, PR China.
| | - Jun Cheng
- College of Mathematics and Statistics, Guangxi Normal University, Guilin, Guangxi, 541004, PR China.
| | - Kaibo Shi
- School of Information Science and Engineering, Chengdu University, Chengdu, Sichuan, 610106, PR China.
| | - Cuiyu Hu
- College of Science, Guilin University of Technology, Guilin, Guangxi, 541004, PR China.
| | - Jindan Lan
- College of Science, Guilin University of Technology, Guilin, Guangxi, 541004, PR China.
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Guo Y, Zhang Y, Wu Y. Almost sure exponential synchronization of network systems under a new intermittent noise-diffusion layer. Neurocomputing 2021. [DOI: 10.1016/j.neucom.2021.05.080] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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Ning D, Fan Z, Wu X, Han X. Interlayer synchronization of duplex time-delay network with delayed pinning impulses. Neurocomputing 2021. [DOI: 10.1016/j.neucom.2021.04.041] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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Chen H, Zhang C, Xu Q, Feng Y. Graph-Theoretic Method on Topology Identification of Stochastic Multi-weighted Complex Networks with Time-Varying Delayed Coupling Based on Adaptive Synchronization. Neural Process Lett 2021. [DOI: 10.1007/s11063-021-10625-4] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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Yan H, Zhou J, Li W, Lu JA, Fan R. Superdiffusion criteria on duplex networks. CHAOS (WOODBURY, N.Y.) 2021; 31:073108. [PMID: 34340319 DOI: 10.1063/5.0042155] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/28/2020] [Accepted: 06/15/2021] [Indexed: 06/13/2023]
Abstract
Diffusion processes widely exist in nature. Some recent papers concerning diffusion processes focus their attention on multiplex networks. Superdiffusion, a phenomenon by which diffusion processes converge to equilibrium faster on multiplex networks than on single networks in isolation, may emerge because diffusion can occur both within and across layers. Some studies have shown that the emergence of superdiffusion depends on the topology of multiplex networks if the interlayer diffusion coefficient is large enough. This paper proposes some superdiffusion criteria relating to the Laplacian matrices of the two layers and provides a construction mechanism for generating a superdiffusible two-layered network. The method we proposed can be used to guide the discovery and construction of superdiffusible multiplex networks without calculating the second smallest Laplacian eigenvalues.
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Affiliation(s)
- Huibiao Yan
- School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
| | - Jin Zhou
- School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
| | - Weiqiang Li
- School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
| | - Jun-An Lu
- School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
| | - Ruguo Fan
- Economics and Management School, Wuhan University, Wuhan 430072, China
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Song K, Li G, Chen X, Deng L, Xiao G, Zeng F, Pei J. Target Controllability of Two-Layer Multiplex Networks Based on Network Flow Theory. IEEE TRANSACTIONS ON CYBERNETICS 2021; 51:2699-2711. [PMID: 30990210 DOI: 10.1109/tcyb.2019.2906700] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
In this paper, we consider the target controllability of two-layer multiplex networks, which is an outstanding challenge faced in various real-world applications. We focus on a fundamental issue regarding how to allocate a minimum number of control sources to guarantee the controllability of each given target subset in each layer, where the external control sources are limited to interact with only one layer. It is shown that this issue is essentially a path cover problem, which is to locate a set of directed paths denoted as P and cycles denoted as C to cover the target sets under the constraint that the nodes in the second layer cannot be the starting node of any element in P , and the number of elements in P attains its minimum. In addition, the formulated path cover problem can be further converted into a maximum network flow problem, which can be efficiently solved by an algorithm called maximum flow-based target path-cover (MFTP). We rigorously prove that MFTP provides the minimum number of control sources for guaranteeing the target controllability of two-layer multiplex networks. It is anticipated that this paper would serve wide applications in target control of real-life networks.
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Wang Z, Xia C, Chen Z, Chen G. Epidemic Propagation With Positive and Negative Preventive Information in Multiplex Networks. IEEE TRANSACTIONS ON CYBERNETICS 2021; 51:1454-1462. [PMID: 31940584 DOI: 10.1109/tcyb.2019.2960605] [Citation(s) in RCA: 38] [Impact Index Per Article: 12.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/08/2023]
Abstract
We propose a novel epidemic model based on two-layered multiplex networks to explore the influence of positive and negative preventive information on epidemic propagation. In the model, one layer represents a social network with positive and negative preventive information spreading competitively, while the other one denotes the physical contact network with epidemic propagation. The individuals who are aware of positive prevention will take more effective measures to avoid being infected than those who are aware of negative prevention. Taking the microscopic Markov chain (MMC) approach, we analytically derive the expression of the epidemic threshold for the proposed epidemic model, which indicates that the diffusion of positive and negative prevention information, as well as the topology of the physical contact network have a significant impact on the epidemic threshold. By comparing the results obtained with MMC and those with the Monte Carlo (MC) simulations, it is found that they are in good agreement, but MMC can well describe the dynamics of the proposed model. Meanwhile, through extensive simulations, we demonstrate the impact of positive and negative preventive information on the epidemic threshold, as well as the prevalence of infectious diseases. We also find that the epidemic prevalence and the epidemic outbreaks can be suppressed by the diffusion of positive preventive information and be promoted by the diffusion of negative preventive information.
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Jin X, Wang Z, Feng Y, Lu Y, Huang C, Zheng C. Impulsive quasi-containment control in heterogeneous multiplex networks. Neurocomputing 2021. [DOI: 10.1016/j.neucom.2020.08.045] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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Synchronization of delayed dynamical networks with multi-links via intermittent pinning control. Neural Comput Appl 2019. [DOI: 10.1007/s00521-019-04614-x] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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