First spiking dynamics of stochastic neuronal model with optimal control

Abstract

First-spiking dynamics of optimally controlled neuron under stimulation of colored noise is investigated. The stochastic averaging principle is utilized and the model equation is approximated by diffusion process and depicted by Itô stochastic differential equation. The control problems for maximizing the resting probability and maximizing the time to first spike are constructed and the dynamical programming equations associated with the corresponding optimization problem are established. The optimal control law is determined. The corresponding backward Kolmogorov equation and Pontryagin equation are established and solved to yield the resting probability and the time to first spike. The analytical results are verified by Monte Carlo simulation. It has shown that the proposed control strategy can suppress the overactive neuronal firing activity and possesses potential application for some neural diseases treatment. © 2009 Springer Berlin Heidelberg.