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

Jan Haskovec, Ioannis Markou

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

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.
Original languageEnglish (US)
Pages (from-to)795-813
Number of pages19
JournalKinetic and Related Models
Volume13
Issue number4
DOIs
StatePublished - Aug 13 2020

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation

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