Exponential asymptotic flocking in the Cucker-Smale model with distributed reaction delays
Type
ArticleAuthors
Haskovec, JanMarkou, Ioannis
Date
2020-08-25Online Publication Date
2020-08-25Print Publication Date
2020Submitted Date
2020-05-13Permanent link to this record
http://hdl.handle.net/10754/665370
Metadata
Show full item recordAbstract
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.Citation
Haskovec, J., & Markou, I. (2020). Exponential asymptotic flocking in the Cucker-Smale model with distributed reaction delays. Mathematical Biosciences and Engineering, 17(5), 5651–5671. doi:10.3934/mbe.2020304Sponsors
JH acknowledges the support of the KAUST baseline funds. IM was funded by the project ARCHERS - Stavros Niarchos Foundation - IACM.arXiv
2005.04657Additional Links
http://www.aimspress.com/article/10.3934/mbe.2020304ae974a485f413a2113503eed53cd6c53
10.3934/MBE.2020304
Scopus Count
Except where otherwise noted, this item's license is described as This is an open access article distributed under the terms of the Creative Commons Attribution License.