Flocking estimates for the Cucker-Smale model with time lag and hierarchical leadership

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:464

Article

Pignotti, Cristina¹  Vallejo, Irene Reche² 

[1] Univ Aquila, Dipartimento Ingn & Sci Informaz & Matemat, Via Vetoio, I-67010 Laquila, Italy

[2] Univ Aquila, MathMods Program, Via Vetoio, I-67010 Laquila, Italy

关键词: Cucker-Smale model;    Flocking;    Time delay;   

DOI  :  10.1016/j.jmaa.2018.04.070

来源: Elsevier

【 摘 要 】

We analyze the Cucker-Smale model under hierarchical leadership in presence of a time delay. By using a Lyapunov functional approach and some induction arguments we will prove convergence to consensus for every positive delay T. We also prove a flocking estimate in the case of a free-will leader. These results seem to point out the advantage of a hierarchical structure in order to contrast time delay effects that frequently appear in real situations. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free