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

TL;DR

This paper investigates how time delays affect the convergence to consensus in the finite-dimensional Cucker-Smale model, providing conditions under which consensus is achieved using Lyapunov functionals.

Contribution

It extends the analysis of the Cucker-Smale model by incorporating time delays and establishing convergence results for both symmetric and nonsymmetric communication weights.

Findings

Convergence to consensus is proven under certain structural conditions.

Both symmetric and nonsymmetric weights are considered.

Lyapunov functionals are used to establish convergence.

Abstract

We consider the celebrated Cucker-Smale model in finite dimension, modelling interacting collective dynamics and their possible evolution to consensus. The objective of this paper is to study the effect of time delays in the general model. By a Lyapunov functional approach, we provide convergence results to consensus for symmetric as well as nonsymmetric communication weights under some structural conditions.