Communications in Mathematical Sciences

Volume 21 (2023)

Number 5

The delayed Cucker–Smale model with attractive power-law potentials

Pages: 1321 – 1332

DOI: https://dx.doi.org/10.4310/CMS.2023.v21.n5.a6

Authors

Long Nie (Department of Mathematics, School of Mathematics and Computer Science, Nanchang University, Nanchang, Jiangxi, China)

Zili Chen (Department of Mathematics, School of Mathematics and Computer Science, Nanchang University, Nanchang, Jiangxi, China)

Abstract

We study the large-time behavior of the delayed Cucker–Smale model with attractive power-law potentials. By making full use of the energy fluctuation and another Lyapunov functional involving the communication function, it is proved that this model achieves consensus, i.e. velocity difference and space diameter converge to zero. More importantly, the precise convergence rate is established.

Keywords

Cucker–Smale model, time delay, consensus

2010 Mathematics Subject Classification

35F25, 35J05, 35Q83, 82C40

Received 17 November 2021

Received revised 12 October 2022

Accepted 13 October 2022

Published 30 August 2023