Decision making in noisy bistable switches A local analysis for non local predictions

In this paper, we try to estimate some statistics about the decision making process in a bistable model submitted to noise by studying the local properties of the system around an hyperbolic saddle point. Despite the fact that the saddle is not an equilibrium point of the stochastic system, we show that a local approach is still instructive. Under appropriate assumptions, the system can be reduced to an Orsntein-Uhlenbeck process whose dynamics depend on the properties of the saddle point. Yet, Orstein-Uhlenbeck processes have been used to study decision making under uncertainty in a broad variety of fields including statistics and cognitive neurosciences .