On the dynamics of a stochastic nonlinear mean-field model

The dynamics of a model introduced by Kometani and Shimizu is studied in the limit of the number of particles going to infinity. In addition to the cumulant expansion already considered by Desai and Zwanzig, we study the low diffusion constant approximation. Both methods present difficulties when the initial condition corresponds to a bistable situation. For this case, we apply Suzuki's ideas and we get a correct description of the evolution, at least at a qualitative level.