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In this paper, we study a two-species model in the form of a coupled systemof nonlinear stochastic differential equations (SDEs) that arises from avariety of applications such as aggregation of biological cells and pedestrianmovements. The evolution of each process is influenced by four differentforces, namely an external force, a self-interacting force, a cross-interactingforce and a stochastic noise where the two interactions depend on the laws ofthe two processes. We also consider a many-particle system and a (nonlinear)partial differential equation (PDE) system that associate to the model. Weprove the wellposedness of the SDEs, the propagation of chaos of the particlesystem, and the existence and (non)-uniqueness of invariant measures of the PDEsystem.

Coupled McKean-Vlasov diffusions: wellposedness, propagation of chaos and invariant measures