Communications in Mathematical Sciences

Volume 21 (2023)

Number 8

Flocking behavior of the Cucker–Smale model under a general digraph on the infinite cylinder

Pages: 2329 – 2339

(Fast Communication)

DOI: https://dx.doi.org/10.4310/CMS.2023.v21.n8.a11

Authors

Xiaoyu Li (School of Science, Nanjing University of Posts and Telecommunications, Nanjing, China)

Lining Ru (School of Mathematical Sciences, Suzhou University of Science and Technology, Suzhou, China)

Abstract

In this paper, we generalize the Cucker–Smale model under a general digraph on the infinite cylinder with the help of the Lie group structure of the infinite cylinder and study the flocking behavior of this model. We show that for $0 \leq \beta \lt 1 / (2h)$ unconditional flocking occurs, where h is the shortest height of the spanning trees of the digraph, and conditional flocking occurs for $\beta \geq 1 / (2h)$ under some conditions depending only on the initial data.

Keywords

Cucker–Smale model, flocking behavior, digraph, infinite cylinder

2010 Mathematics Subject Classification

92D25, 93Axx

Full Text (PDF format)

Received 27 December 2022

Received revised 12 August 2023

Accepted 25 August 2023

Published 15 November 2023