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    A Cucker--Smale Model with Noise and Delay

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    Type
    Article
    Authors
    Erban, Radek
    Haskovec, Jan cc
    Sun, Yongzheng
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Date
    2016-08-09
    Online Publication Date
    2016-08-09
    Print Publication Date
    2016-01
    Permanent link to this record
    http://hdl.handle.net/10754/622022
    
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    Abstract
    A generalization of the Cucker-Smale model for collective animal behavior is investigated. The model is formulated as a system of delayed stochastic differential equations. It incorporates two additional processes which are present in animal decision making, but are often neglected in modeling: (i) stochasticity (imperfections) of individual behavior and (ii) delayed responses of individuals to signals in their environment. Sufficient conditions for flocking for the generalized Cucker-Smale model are derived by using a suitable Lyapunov functional. As a by-product, a new result regarding the asymptotic behavior of delayed geometric Brownian motion is obtained. In the second part of the paper, results of systematic numerical simulations are presented. They not only illustrate the analytical results, but hint at a somehow surprising behavior
    Citation
    Erban R, Haškovec J, Sun Y (2016) A Cucker--Smale Model with Noise and Delay. SIAM Journal on Applied Mathematics 76: 1535–1557. Available: http://dx.doi.org/10.1137/15M1030467.
    Sponsors
    The authors would like to thank the Isaac Newton Institute for Mathematical Sciences, Cambridge, for support and hospitality during the programme
    Publisher
    Society for Industrial & Applied Mathematics (SIAM)
    Journal
    SIAM Journal on Applied Mathematics
    DOI
    10.1137/15M1030467
    arXiv
    1507.04432
    Additional Links
    http://epubs.siam.org/doi/10.1137/15M1030467
    ae974a485f413a2113503eed53cd6c53
    10.1137/15M1030467
    Scopus Count
    Collections
    Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

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