On the asymptotic persistency of a bi-cluster flocking in a Cucker-Smale ensemble

We study the asymptotic dynamics of Cucker-Smale (CS) type model with unit speed constraint and attractive-repulsive couplings. For this, we provide several sufficient frameworks leading to bi-cluster flocking asymptotically in which the whole ensemble is asymptotically separated into two flocking sub-ensembles. From the modeling perspective, intra and inter couplings are assumed to be attractive (positive) and repulsive (negative), respectively. Under the proposed frameworks, relative velocities in the same cluster tend to zero, whereas relative positions in each sub-ensemble are also uniformly bounded and distances between different ensembles diverge to infinity asymptotically. We also provide several numerical simulations and compare them with our analytical results.