Analytical determination of firing times in stochastic nonlinear neural models

We present for the #rst time an analytical approach for determining the time of #ring of nonlinear stochastic neuronal models. The theory of Markov processes is applied to the Fitzhugh–Nagumo system with a constant mean, Gaussian white noise input, representing stochastic excitation and inhibition. An equation obtained for the mean of the time to #rst spike is solved by means of an accurate one-dimensional approximation. Veri#cation of the method is obtained through the excellent agreement between the moments of the #ring time found by numerical solution of di6erential equations and those obtained by simulation of the solutions of the model stochastic di6erential equations. We also #nd a maximum at small noise values which constitutes a form of stochastic resonance. c © 2002 Elsevier Science B.V. All rights reserved.