Emergent behavior of Cucker-Smale flocking particles with time delays

TL;DR

This paper investigates how time delays in the interactions of Cucker-Smale flocking particles affect their collective behavior, providing conditions under which flocking still occurs despite delays.

Contribution

It introduces a new analysis framework for Cucker-Smale models with multiple constant delays, establishing sufficient conditions for flocking with small delays.

Findings

Flocking behavior persists under small maximum delays.

A system of dissipative differential inequalities is used for analysis.

Conditions for flocking depend on delay magnitude.

Abstract

We analyze Cucker-Smale flocking particles with delayed coupling, where different constant delays are considered between particles. By constructing a system of dissipative differential inequalities together with a continuity argument, we provide a sufficient condition for the flocking behavior when the maximum value of time delays is sufficiently small.