# Mean-field analysis of multi-population dynamics with label switching

## TL;DR

This paper develops a mean-field framework for analyzing multi-population agent models with label switching, establishing well-posedness and extending results in leader-follower dynamics.

## Contribution

It introduces a general functional analytic approach for multi-population models with label switching, including discrete and continuous labels, and generalizes existing leader-follower results.

## Key findings

- Established well-posedness of the model
- Provided concrete applications for discrete and continuous labels
- Generalized previous leader-follower dynamics results

## Abstract

The mean-field analysis of a multi-population agent-based model is performed. The model couples a particle dynamics driven by a nonlocal velocity with a Markow-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 case of discrete and continuous set of labels. In the particular case of a leader-follower dynamics, the existence and approximation results recently obtained in [2] are recovered and generalized as a byproduct of the abstract approach proposed.