ASYMPTOTIC FLOCKING IN THE CUCKER-SMALE MODEL WITH REACTION-TYPE DELAYS IN THE NON-OSCILLATORY REGIME
Embargo End Date2021-08-13
Permanent link to this recordhttp://hdl.handle.net/10754/670126
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AbstractWe 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.
CitationHaskovec, 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
SponsorsThe first author is supported by KAUST baseline funds
JournalKINETIC AND RELATED MODELS