Asymptotic dynamics for the Cucker-Smale model with velocity control

TL;DR

This paper analyzes the long-term behavior of a generalized Cucker-Smale model with velocity control, demonstrating conditions for flocking, clustering, and collision avoidance, including models with singular communication weights.

Contribution

It introduces a unified framework for various Cucker-Smale models with velocity control, providing new insights into their asymptotic dynamics and collision avoidance mechanisms.

Findings

Established conditions for mono and bi-cluster flocking.

Proved positive lower bounds for agent distances under singular weights.

Unified analysis encompassing multiple Cucker-Smale variants.

Abstract

We study the Cucker-Smale model with a velocity control function. The Cucker-Smale model design the emergence of consensus in terms of flocking. A proposed model encompasses several Cucker-Smale models, such as a speed limit model, a relativistic model, and an almost unit speed model. We provide collective behaviors of the proposed model, like mono or bi-cluster flocking, sticking, and collision avoidance, depending on the regularity and singularity of communication weight at the origin. In particular, we provide a sufficient framework to guarantee a positive lower bound of the distance between agents under strongly singular communications.