The relaxation time of processes in a FitzHugh–Nagumo neural system with time delay

Abstract

In this paper, we study the relaxation time (RT) of the steady-state correlation function in a FitzHugh–Nagumo neural system under the presence of multiplicative and additive white noises and time delay. The noise correlation parameter λ can produce a critical behavior in the RT as functions of the multiplicative noise intensity D, the additive noise intensity Q and the time delay τ. That is, the RT decreases as the noise intensities D and Q increase, and increases as the time delay τ increases below the critical value of λ. However, above the critical value, the RT first increases, reaches a maximum, and then decreases as D, Q and τ increase, i.e. a noise intensity D or Q and a time delay τ exist, at which the time scales of the relaxation process are at their largest. In addition, the additive noise intensity Q can also produce a critical behavior in the RT as a function of λ. The noise correlation parameter λ first increases the RT of processes, then decreases it below the critical value of Q. Above the critical value, λ increases it.