Convergence of velocities for the short range communicated discrete-time Cucker–Smale model

Xiuxia Yin, Zhiwei Gao*, Dong Yue*, Yichuan Fu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Most existing literature about the discrete-time Cucker−Smale model focus on the asymptotic flocking behavior. When the communication weight has a long range, asymptotic flocking holds for any initial data. Actually, the velocity of every agent will exponentially converge to the same limit in this case. However, when the communication weight has a short range, asymptotic flocking does not exist for general initial data. In this note, we will prove the convergence of velocities for any initial data in the short range communication case. We first propose a new strategy about the convergence of velocities, and then show an important inequality about the velocity–position moment, according to which we will successfully prove the convergence of velocities and obtain the convergence rates for two kinds of communication weights. Besides, for some special initial data we show that the limits of velocities can be different from each other. Simulation results are given to validate the theoretical results.

Original languageEnglish
Article number109659
Number of pages7
JournalAutomatica
Volume129
Early online date3 May 2021
DOIs
Publication statusPublished - 1 Jul 2021

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