@article{Xu2022, 
author = {Qin Xu and Xiao Wang and Yicheng Liu},
title = {Emergent behavior of Cucker–Smale model with time-varying topological structures and reaction-type delays},
year = {2022},
journal = {Mathematical Modelling and Control},
volume = {2},
number = {4},
pages = {200-218},
keywords = {flocking, time delay, Cucker–Smale model, time-varying topological structures, persistence of excitation},
url = {https://www.sciopen.com/article/10.3934/mmc.2022020},
doi = {10.3934/mmc.2022020},
abstract = {This paper studies the continuous Cucker–Smale model with time-varying topological structures and reaction-type delay. The goal of this paper is to establish a sufficient framework for flocking behaviors. Our method combines strict Lyapunov design with the derivation of an appropriate persistence condition for multi-agent systems. First, to prove that position fluctuations are uniformly bounded, a strict and trajectory-dependent Lyapunov functional is constructed via reparametrization of the time variable. Then, by constructing a global Lyapunov functional and using a novel backward-forward estimate, it is deduced that velocity fluctuations converge to zero. Finally, flocking behaviors are analyzed separately in terms of time delays and communication failures.}
}