Flocking in noisy environments

TL;DR

This paper studies how groups of agents can still achieve alignment in noisy environments by analyzing a perturbed flocking model and providing probabilistic guarantees of near-alignment.

Contribution

It extends the Cucker-Smale flocking model to noisy conditions and proves probabilistic near-alignment results under similar assumptions.

Findings

Nearly-alignment is achieved with high probability in noisy environments.

The model demonstrates robustness of flocking behavior despite perturbations.

Probabilistic bounds are established for the emergence of collective alignment.

Abstract

We consider a perturbed version of the dynamics of a flock introduced by Cucker and Smale ("Emergent behaviour in flocks") and prove, under similar conditions, that nearly-alignment (a concept that is precised in the text) is achieved with a certain probability, bounded from below.