Engineers and neuroscientists generally believe that noise is something to be avoided in information systems. In this paper we show that noise, in fact, can be an important element in the translation of neuronal generator potentials (summed inputs) to neuronal spike trains (outputs), creating or expanding a range of amplitudes over which the spike rate is proportional to the generator potential amplitude. Noise converts the basically nonlinear operation of a spike initiator into a nearly linear modulation process. This linearization effect of noise is examined in a simple intuitive model of a static threshold and in a more realistic computer simulation of a spike initiator based on the Hodgkin-Huxley (HH) model. The results are qualitatively similar; in each case larger noise amplitude results in a larger range of nearly-linear modulation. The computer simulation of the HH model with noise shows linear and nonlinear features that we earlier had observed in spike data obtained from the VIIIth nerve of the bullfrog. This suggests that these features can be explained in terms of spike initiator properties, and it also suggests that the HH model may be useful for representing basic spike initiator properties in vertebrates.

In this paper, the first-passage behavior of under-damped asymmetric bistable system driven by Lévy noise is studied. The two aspects considered are the mean first-passage time (MFPT) and the distribution of first-passage time in two opposite directions. To begin with, using the Janicki–Weron algorithm to generate Lévy noise, the system driven by Lévy noise is simulated through the fourth-order Runge–Kutta algorithm. Then the first-passage time of [Formula: see text] response tracks is calculated, and the MFPT and the distribution of first-passage time are obtained. Finally, the influence of Lévy noise and system parameters on MFPT and the distribution of first-passage time are analyzed. Moreover, the noise enhanced stability (NES) effect is found.

In this paper, the dynamical behavior of the FitzHugh–Nagumo (FHN) neural system with time delay driven by Lévy noise is studied from two aspects: the mean first-passage time (MFPT) and the probability density function (PDF) of the first-passage time (FPT). Using the Janicki–Weron algorithm to generate the Lévy noise, and through the order-4 Runge–Kutta algorithm to simulate the FHN system response, the time that the system needs from one stable state to the other one is tracked in the process. Using the MATLAB software to simulate the process above 20,000 times and recording the PFTs, the PDF of the FPT and the MFPT is obtained. Finally, the effects of the Lévy noise and time-delay on the FPT are discussed. It is found that the increase of both time-delay feedback intensity and Lévy noise intensity can promote the transition of the particle from the resting state to the excited state. However, the two parameters produce the opposite effects in the other direction.