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

License
http://creativecommons.org/licenses/by/4.0

Type
Article

Authors
Haskovec, Jan
Markou, Ioannis

KAUST Department
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Online Publication Date
2020-08-25

Print Publication Date
2020

Date
2020-08-25

Submitted Date
2020-05-13

Abstract
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.2020304

Acknowledgements
JH acknowledges the support of the KAUST baseline funds. IM was funded by the project ARCHERS - Stavros Niarchos Foundation - IACM.

Publisher
American Institute of Mathematical Sciences (AIMS)

Journal
Mathematical Biosciences and Engineering

DOI
10.3934/MBE.2020304

arXiv
2005.04657

Additional Links
http://www.aimspress.com/article/10.3934/mbe.2020304

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