Georgia Institute of Technology College of Sciences

I will consider mathematical models of decision making based on dynamics in the neighborhood of unstable equilibria and involving random perturbations due to small noise. I will report results on the vanishing noise limit for these systems, providing precise predictions about the statistics of decision making times and sequences of unstable equilibria visited by the process. Mathematically, the results are based on the analysis of random Poincare maps in the neighborhood of each equilibrium point. I will discuss applications to neuroscience and psychology along with some experimental data.