Emergence of bi-cluster flocking for agent-based models with unit speed constraint

We study the emergence of bi-cluster flocking for a generalized Justh-Krishnaprasad (J-K) model and the Cucker-Smale (C-S) model with the unit speed constraint. We provide a sufficient framework for the emergence of bi-cluster flocking in terms of initial configurations and communication weights between agents. Our analytical results on bi-cluster flocking illustrate that the spatial-decay rate of communication weights is transferred to the temporal decay rate toward the bi-cluster flocking configuration. We also provide several numerical simulations and compare them to our analytical results.