Robustness of multi-cluster flocking and uniform-in-time transition for the discrete Motsch–Tadmor model

We study the robustness and uniform-in-time transition for multi-cluster flocking phenomena of the discrete Motsch–Tadmor (DMT) model. The DMT model corresponds to the discrete Cucker–Smale (DCS) model with a normalized communication weight. For an $ m $-cluster DMT model, we propose a sufficient framework on the robustness of multi-cluster flocking and uniform-in-time transition to the corresponding continuous Motsch–Tadmor (MT) model as the time step tends to zero. We also provide several numerical simulations and compare them with analytical results.