Mean-field Analysis of Multipopulation Dynamics with Label Switching

The mean-field analysis of a multipopulation agent-based model is performed. The model couples a particle dynamics driven by a nonlocal velocity with a Markov-type jump process on the probability that each agent has of belonging to a given population. A general functional analytic framework for the well-posedness of the problem is established, and some concrete applications are presented, both in the cases of a discrete and continuous set of labels. In the particular case of a leader-follower dynamics, the existence and approximation results recently obtained in [G. Albi et al., Math. Models Methods Appl. Sci., 29 (2019), pp. 633--679] are recovered and generalized as a byproduct of the abstract approach proposed.