ASYMPTOTIC FLOCKING IN THE CUCKER-SMALE MODEL WITH REACTION-TYPE DELAYS IN THE NON-OSCILLATORY REGIME
Type
ArticleAuthors
Haskovec, JanMarkou, Ioannis
Date
2020-08-13Embargo End Date
2021-08-13Permanent link to this record
http://hdl.handle.net/10754/670126
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Show full item recordAbstract
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.2020027Sponsors
The first author is supported by KAUST baseline fundsJournal
Kinetic & Related ModelsarXiv
1810.01084Additional Links
http://aimsciences.org//article/doi/10.3934/krm.2020027http://arxiv.org/pdf/1810.01084
ae974a485f413a2113503eed53cd6c53
10.3934/krm.2020027