In this paper, we study a two-species model in the form of a coupled system of nonlinear stochastic differential equations (SDEs) that arises from a variety of applications such as aggregation of biological cells and pedestrian movements. The evolution of each process is influenced by four different forces, namely an external force, a self-interacting force, a cross-interacting force and a stochastic noise where the two interactions depend on the laws of the two processes. We also consider a many-particle system and a (nonlinear) partial differential equation (PDE) system that associate to the model. We prove the wellposedness of the SDEs, the propagation of chaos of the particle system, and the existence and (non)-uniqueness of invariant measures of the PDE system.
|Journal||Stochastics: an international journal of probablity and stochastic processes|
|Early online date||22 Oct 2019|
|Publication status||E-pub ahead of print - 22 Oct 2019|
- interacting particle systems
- McKean-Vlasov dynamics
- propagation of chaos
- invariant measures