Finite-time flocking of an infinite set of Cucker-Smale particles with sublinear velocity couplings

TL;DR

This paper establishes conditions under which an infinite set of particles following the Cucker-Smale model achieve finite-time flocking, providing explicit alignment-time estimates for fixed and switching networks.

Contribution

It introduces a component-wise diameter framework for finite-time flocking analysis applicable to both finite and infinite systems with sublinear velocity couplings.

Findings

Finite-time flocking occurs under certain conditions for fixed sender networks.

Flocking persists under switching sender networks with mild influence assumptions.

Alignment-time estimates are independent of the number of agents.

Abstract

We study finite-time flocking for an infinite set of Cucker-Smale particles with sublinear velocity coupling under fixed and switching sender networks. For this, we use a component-wise diameter framework and exploit sub-linear dissipation mechanisms, and derive sufficient conditions for finite-time flocking equipped with explicit alignment-time estimate. For a fixed sender network, we establish component-wise finite-time flocking results under both integrable and non-integrable communication weights. When communication weight function is non-integrable, finite-time flocking is guaranteed for any bounded initial configuration. We further extend the flocking analysis to switching sender networks and show that finite-time flocking persists under mild assumptions on the cumulative influence of time-varying sender weights. The proposed framework is also applicable to both finite and infinite systems, and it yields alignment-time estimates that do not depend on the number of agents.