Dynamics of a FitzHugh-Nagumo system driven by a periodic signal in the presence of colored noise

Abstract

We analyze the dynamics of a FitzHugh-Naguno system, driven by a periodic signal, in the presence of coloured noise. We consider the effects of the fluctuations by inserting in the deterministic FitzHugh-Nagumo model a term of additive Gaussian noise. We study the system in two different cases: the fluctuations affect the dynamics of the membrane potential (CASE I), the recovery variable is subjected to noise (CASE II). We review briefly the effects of the white noise, responsible for the appearance of resonant activation (RA) and noise enhanced stability (NES) phenomena. Afterwards we study the two cases in the presence of a coloured noise with correlation time tau. We investigate the effects of the coloured noise on the neuron dynamics for different values of the correlation time. We find that the positions both of the minimwn of RA and the maximwn of NES change as a function of tau.