Author:
Xu Qin,Wang Xiao,Liu Yicheng
Abstract
<abstract><p>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.</p></abstract>
Publisher
American Institute of Mathematical Sciences (AIMS)
Reference40 articles.
1. F. Cucker, S. Smale, Emergent behavior in flocks, IEEE Trans. Automat. Control, 52 (2007), 852–862. https://doi.org/10.1109/TAC.2007.895842
2. F. Cucker, S. Smale, On the mathematics of emergence, Jpn. J. Math., 2 (2007), 197–227. https://doi.org/10.1007/s11537-007-0647-x
3. S. Motsch, E. Tadmor, Heterophilious dynamics enhances consensus, SIAM Rev., 56 (2014), 577–621. https://doi.org/10.1137/120901866
4. T. Vicsek, A. Czirók, E. Ben-Jacob, I. Cohen, O. Shochet, Novel type of phase transition in a system of self-driven particles, Phys. Rev. Lett., 75 (1995), 1226–1229. https://doi.org/10.1103/physrevlett.75.1226
5. Y.-P. Choi, S.-Y. Ha, Z. Li, Emergent dynamics of the Cucker–Smale flocking model and its variants, Birkhäuser, Cham, 2017. https://doi.org/10.1007/978-3-319-49996-3_8