Flocking in the Cucker-Smale model with self-delay and nonsymmetric interaction weights

TL;DR

This paper establishes conditions under which flocking behavior emerges in the Cucker-Smale model considering self-delay and non-symmetric interactions, highlighting the importance of delay length relative to communication decay.

Contribution

It provides a new sufficient condition for asymptotic flocking in the Cucker-Smale model with delays and nonsymmetric weights, using a novel analytical approach.

Findings

Flocking occurs when delay length is small relative to communication decay rate.

Derived a decay estimate for group velocity diameter.

Applied a Gronwall-Halanay inequality variant for proof.

Abstract

We derive a sufficient condition for asymptotic flocking in the Cucker-Smale model with self-delay (also called reaction delay) and with non-symmetric interaction weights. The condition prescribes smallness of the delay length relative to the decay rate of the inter-agent communication weight. The proof is carried out by a bootstrapping argument combining a decay estimate for the group velocity diameter with a variant of the Gronwall-Halanay inequality.