Models and synchronization of time-delayed complex dynamical networks with multi-links based on adaptive control

Peng, Haipeng; Wei, Nan; Li, Lixiang; Xie, Weisheng; Yang, Yixian

doi:10.1016/j.physleta.2010.03.052

Cited by 50 publications

(21 citation statements)

References 32 publications

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“…Multiplex networks, as a typical kind of multilayer network structure, can be regarded as the combination of several network layers, which contain the same nodes (or share at least some fraction of nodes) yet different intra-layer connections [203,231,240,241,[338][339][340][341][342][343][344][356][357][358]. For each node, we term its counterpart in every layer as a 'replica'.…”

Section: Vaccination On Multiplex Networkmentioning

confidence: 99%

Statistical physics of vaccination

et al. 2016

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Historically, infectious diseases caused considerable damage to human societies, and they continue to do so today. To help reduce their impact, mathematical models of disease transmission have been studied to help understand disease dynamics and inform prevention strategies. Vaccination-one of the most important preventive measures of modern times-is of great interest both theoretically and empirically. And in contrast to traditional approaches, recent research increasingly explores the pivotal implications of individual behavior and heterogeneous contact patterns in populations. Our report reviews the developmental arc of theoretical epidemiology with emphasis on vaccination, as it led from classical models assuming homogeneously mixing (mean-field) populations and ignoring human behavior, to recent models that account for behavioral feedback and/or population spatial/social structure. Many of the methods used originated in statistical physics, such as lattice and network models, and their associated analytical frameworks. Similarly, the feedback loop between vaccinating behavior and disease propagation forms a coupled nonlinear system with analogs in physics. We also review the new paradigm of digital epidemiology, wherein sources of digital data such as online social media are mined for high-resolution information on epidemiologically relevant individual behavior. Armed with the tools and concepts of statistical physics, and further assisted by new sources of digital data, models that capture nonlinear interactions between behavior and disease dynamics offer a novel way of modeling real-world phenomena, and can help improve health outcomes. We conclude the review by discussing open problems in the field and promising directions for future research.

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Section: Vaccination On Multiplex Networkmentioning

confidence: 99%

Statistical physics of vaccination

et al. 2016

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“…Compared with researches of single link networks [30][31][32][33], those of networks with multilinks are more practical and significant. There have been a lot of research achievements in this field so far [34][35][36]. However, to my best knowledge, few put their attention to the hybrid coupled networks with both one single time-varying delay coupling and multilinks.…”

Section: Introductionmentioning

confidence: 99%

Fixed-Time Synchronization for Hybrid Coupled Dynamical Networks with Multilinks and Time-Varying Delays

Qiu

Peng

et al. 2017

Mathematical Problems in Engineering

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This paper concerns the problem of fixed/finite-time synchronization of hybrid coupled dynamical networks. The considered dynamical networks with multilinks contain only one transmittal time-varying delay for each subnetwork, which makes us get hold of more interesting and practical points. Two kinds of delay-dependent feedback controllers with multilinks as well as appropriate Lyapunov functions are defined to achieve the goal of fixed-time synchronization and finite-time synchronization for the networks. Some novel and effective criteria of hybrid coupled networks are derived based on fixed-time and finite-time stability analysis. Finally, two numerical simulation examples are given to show the effectiveness of the results proposed in our paper.

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“…In many practical problems, it often happens that the states of the system cannot be observed directly. Instead, we can only observe the states of the system with nonlinear coupled, which means that the coupling scheme is nonlinear [15][16][17][18][19][20]. In addition, in practical situations, there exists much uncertain information in complex networks, such as the topological structures, for example, genomic coexpression networks, energy network, biological neural networks, and so on.…”

Section: Introductionmentioning

confidence: 99%

Mean Square Synchronization of Stochastic Nonlinear Delayed Coupled Complex Networks

Xie¹,

Xu²,

Tong

2013

Discrete Dynamics in Nature and Society

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We investigate the problem of adaptive mean square synchronization for nonlinear delayed coupled complex networks with stochastic perturbation. Based on the LaSalle invariance principle and the properties of the Weiner process, the controller and adaptive laws are designed to ensure achieving stochastic synchronization and topology identification of complex networks. Sufficient conditions are given to ensure the complex networks to be mean square synchronization. Furthermore, numerical simulations are also given to demonstrate the effectiveness of the proposed scheme.

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Models and synchronization of time-delayed complex dynamical networks with multi-links based on adaptive control

Cited by 50 publications

References 32 publications

Statistical physics of vaccination

Statistical physics of vaccination

Fixed-Time Synchronization for Hybrid Coupled Dynamical Networks with Multilinks and Time-Varying Delays

Mean Square Synchronization of Stochastic Nonlinear Delayed Coupled Complex Networks

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