STOCHASTIC SINGLE NEURONS

We study the stochastic behavior of a single self-exciting model neuro n with additive noise, a system that has bistable stochastic dynamics. We use Langevin and Fokker-Planck equations to obtain analytical expr essions for the stationary distribution of activities and for the cros sing rate between two stable states. We adjust the parameters in these expressions to fit observed histograms of neural activity, thus obtai ning what we call an ''effective single neuron'' for a given network. We construct an effective single neuron from an activity histogram of a representative hidden neuron in a recurrent learning network. We als o compare our result with an effective single neuron previously obtain ed analytically through the adiabatic elimination approximation.