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We study a Fokker-Planck equation modelling the firing rates of twointeracting populations of neurons. This model arises in computationalneuroscience when considering, for example, bistable visual perception problemsand is based on a stochastic Wilson-Cowan system of differential equations. Ina previous work, the slow-fast behavior of the solution of the Fokker-Planckequation has been highlighted. Our aim is to demonstrate that the complexity ofthe model can be drastically reduced using this slow-fast structure. In fact,we can derive a one-dimensional Fokker-Planck equation that describes theevolution of the solution along the so-called slow manifold. This permits tohave a direct efficient determination of the equilibrium state and itseffective potential, and thus to investigate its dependencies with respect tovarious parameters of the model. It also allows to obtain information about thetime escaping behavior. The results obtained for the reduced 1D equation arevalidated with those of the original 2D equation both for equilibrium andtransient behavior.

One dimensional Fokker-Planck reduced dynamics of decision making models in Computational Neuroscience