Cucker-Smale model with a bonding force and a singular interaction kernel

TL;DR

This paper proves that particles in a modified Cucker-Smale flocking model with bonding forces and singular interactions do not collide asymptotically and remain confined within a bounded region over time.

Contribution

It establishes the global-in-time existence of minimal inter-particle distances and rules out finite-time collisions in the CSB model with singular weights.

Findings

No asymptotic collisions occur between particles.

Finite-time collisions are impossible with singular communication weights.

Particles remain confined within a bounded region over time.

Abstract

We prove the lack of asymptotic collisions between particles following the Cucker-Smale flocking model with a bonding force and its simplification. Moreover, we prove that in the case of the CSB model with a singular communication weight, finite-in-time collisions are impossible. Consequently, we establish existence of the global-in-time minimal distance between the particles. Furthermore, we show that asymptotic distribution of particles is confined within a ball of a given radius.