期刊
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
卷 29, 期 4, 页码 633-679出版社
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218202519400025
关键词
Birth-death process; mean-field limit; analysis of PDE; agent-based systems; numerical modelling
资金
- INdAM-GNCS 2018 project Numerical methods for multiscale control problems
- project MIUR Departments of Excellence 2018-2022
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 scalar-valued transition rates depending nonlinearly on the global state of the system at each time. We first prove the existence and uniqueness of solutions for the leader-follower dynamics, under suitable assumptions. We then establish, for an appropriate choice of the initial datum, the equivalence of the system with a PDE-ODE system, that consists of a continuity equation over the state space and an ODE for the transition from leader to follower or vice versa. We further introduce a stochastic process approximating the PDE, together with a jump process that models the switch 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. Finally, several numerical simulations of social interactions dynamics modeled by our system are discussed.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据