Special Session 100: 

Leader formation with mean-field birth and death models

Mattia Bongini
Universite Paris Dauphine
France
Co-Author(s):    Giacomo Albi, Francesco Rossi, Francesco Solombrino
Abstract:
We provide a mean-field description for a leader-follower dynamics with mass transfer among the two populations. This model allows the transition from followers to leaders and vice versa with transition rates depending nonlinearly on the measures of the two populations. Under certain assumptions on the interaction kernels and the transition rates, we reformulate the problem as a continuity equation over the state space and a system of ODEs for the change of label follower-leader. We then introduce a stochastic process approximating the PDE, together with a jump process over the space of labels that models the transition between the two populations. Using a propagation of chaos argument, we show that the particle system generated by these two processes converges in probability to a solution of the PDE-ODE system. Our approach can be easily generalized to multiple (even countable) populations.