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    ASYMPTOTIC FLOCKING IN THE CUCKER-SMALE MODEL WITH REACTION-TYPE DELAYS IN THE NON-OSCILLATORY REGIME

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    Type
    Article
    Authors
    Haskovec, Jan
    Markou, Ioannis
    KAUST Department
    Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division
    Date
    2020-08-13
    Embargo End Date
    2021-08-13
    Permanent link to this record
    http://hdl.handle.net/10754/670126
    
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    Abstract
    We study a variant of the Cucker-Smale system with reaction-type delay. Using novel backward-forward and stability estimates on appropriate quantities we derive sufficient conditions for asymptotic ocking of the solutions. These conditions, although not explicit, relate the velocity uctuation of the initial datum and the length of the delay. If satisfied, they guarantee monotone decay (i.e., non-oscillatory regime) of the velocity uctuations towards zero for large times. For the simplified setting with only two agents and constant communication rate the Cucker-Smale system reduces to the delay negative feedback equation. We demonstrate that in this case our method provides the sharp condition for the size of the delay such that the solution be non-oscillatory. Moreover, we comment on the mathematical issues appearing in the formal macroscopic description of the reaction-type delay system.
    Citation
    Haskovec, J., & Markou, I. (2020). Asymptotic flocking in the Cucker-Smale model with reaction-type delays in the non-oscillatory regime. Kinetic & Related Models, 13(4), 795–813. doi:10.3934/krm.2020027
    Sponsors
    The first author is supported by KAUST baseline funds
    Publisher
    American Institute of Mathematical Sciences (AIMS)
    Journal
    Kinetic & Related Models
    DOI
    10.3934/krm.2020027
    arXiv
    1810.01084
    Additional Links
    http://aimsciences.org//article/doi/10.3934/krm.2020027
    http://arxiv.org/pdf/1810.01084
    ae974a485f413a2113503eed53cd6c53
    10.3934/krm.2020027
    Scopus Count
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    Articles; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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