Inhibition and modulation of rhythmic neuronal spiking by noise

We investigated the effects of noise on periodic firing in the Hodgkin-Huxley nonlinear system. With mean input current μ as a bifurcation parameter, a bifurcation to repetitive spiking occurs at a critical value μ_c≈6.44 . The firing behavior was studied as a function of the mean and variance of the input current, firstly with initial resting conditions. Noise of a small amplitude can turn off the spiking for values of μ close to μ_c , and the number of spikes undergoes a minimum as a function of the noise level. The robustness of these phenomena was confirmed by simulations with random initial conditions and with random time of commencement of the noise. Furthermore, their generality was indicated by their occurrence when additive noise was replaced by conductance-based noise. For long periods of observation, many frequent transitions may occur from spiking to nonspiking activity when the noise is sufficiently strong. Explanations of the above phenomena are sought in terms of the underlying bifurcation structure and the probabilities that noise shifts the process from the basin of attraction of a stable limit cycle to that of a stable rest state. The waiting times for such transitions depend strongly on the values of μ and σ and on the forms of the basins of attraction. The observed effects of noise are expected to occur in diverse fields in systems with the same underlying dynamical structure.