Exponential asymptotic flocking in the Cucker-Smale model with distributed reaction delays

Jan Haskovec, Ioannis Markou

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


We study a variant of the Cucker-Smale system with distributed reaction delays. Using backward-forward and stability estimates on the quadratic velocity fluctuations we derive sufficient conditions for asymptotic flocking of the solutions. The conditions are formulated in terms of moments of the delay distribution and they guarantee exponential decay of velocity fluctuations towards zero for large times. We demonstrate the applicability of our theory to particular delay distributions - exponential, uniform and linear. For the exponential distribution, the flocking condition can be resolved analytically, leading to an explicit formula. For the other two distributions, the satisfiability of the assumptions is investigated numerically.
Original languageEnglish (US)
Pages (from-to)5651-5671
Number of pages21
JournalMathematical Biosciences and Engineering
Issue number5
StatePublished - Aug 25 2020

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: JH acknowledges the support of the KAUST baseline funds. IM was funded by the project ARCHERS - Stavros Niarchos Foundation - IACM.


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