Communications in Mathematical Sciences

Volume 16 (2018)

Number 8

Convergence to consensus of the general finite-dimensional Cucker–Smale model with time-varying delays

Pages: 2053 – 2076



Cristina Pignotti (Dipartimento di Ingegneria e Scienze dell’Informazione e Matematica, Università di L’Aquila, Italy)

Emmanuel Trélat (Laboratoire Jacques-Louis Lions, Sorbonne Université, Université Paris-Diderot, Paris, France)


We consider the well known finite-dimensional Cucker–Smale system, modelling interacting collective dynamics and their possible convergence to consensus. The objective of this paper is to study the influence of time-delays in the general model on the convergence to consensus. By a Lyapunov functional approach, we establish convergence results to consensus for symmetric and nonsymmetric communication weights under some structural conditions.


consensus models, delay, Lyapunov functions

2010 Mathematics Subject Classification

34D05, 34D20

Received 15 July 2017

Accepted 22 July 2018

Published 18 April 2019