Introduction to mean-field models of particle systems（1、2、3）

Abstract

Particle systems exhibit various dynamics such as collision, interaction, and collective motions that can lead to lots of applications in biology, physics, and engineering. One major modeling strategy is to start with individual-based models that consist of ordinary differential equations describing the dynamics of each particle due to physical laws, and then derive the mean-field and fluid models in the mesoscopic and macroscopic levels. The models in different scales are suitable for certain applications of great interest. We will present the classic theory on the connection between particle models and McKean-Vlasov equations, and discuss the open questions.