| Abstract: |
| We prove the lack of asymptotic collisions between particles following Cucker-Smale flocking model with a bonding force (CSB model) and its simplification. Moreover, we prove that in the case of the CSB model with sufficiently singular communication weight (e.g., $\psi(s)=s^{-\alpha}$ for $\alpha\geq 1$), finite-in-time collisions are impossible. Consequently, we establish existence of the global-in-time minimal distance between the particles. Finally, we present asymptotic distribution of particles which is confined within a ball of given radius. |
|