Collision-free flocking for a time-delay system
type: Item
instance of: scholarly article
title: Collision-free flocking for a time-delay system
zbMATH Open document ID: 1472.34143
author: Maoli Chen
author: Xiao Wang
author: Yicheng Liu
published in: Discrete and Continuous Dynamical Systems. Series B
publication date: 2021-06-03T00:00:00Z
review text: The authors studies a Cucker-Smale type model with two additional mechanism. One is time delay effect, and the other one is the repulsion force when two particles are close. Therefore, the inertial effect is stronger and oscillations appear in the system, which draws difficulty in analysis of large time behavior. Moreover, the mean velocity is no longer conservative, thus the flocking is described via vanishing of relative velocity. The authors first prove global existence of the solution by showing collision avoidance in finite time. Then, when delay is sufficiently small, the authors construct a proper Lyapunov functional to describe the decay structure, and show the emergence of asymptotical flocking based on Barbalat's lemma.
reviewed by: Xiongtao Zhang
Mathematics Subject Classification ID: 34K60
Mathematics Subject Classification ID: 92D50
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 34K25
zbMATH DE Number: 7354175
zbMATH Keywords: measurement delay
zbMATH Keywords: time-asymptotic flocking
zbMATH Keywords: collision avoidance
MaRDI profile type: Publication
full work available at URL: dcdsb.2020251
OpenAlex ID: W3080191423
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DOI: 10.3934/DCDSB.2020251
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description: scientific article; zbMATH DE number 7354175