MiS Preprint Repository

We investigated the effects of noise on the periodic firing activity of the Hodgkin-Huxley nonlinear system. With mean input current $\mu$ as a bifurcation parameter, an Andronov-Hopf bifurcation to repetitive spiking occurs at a critical value ${\mu }_c\approx$ 6.4. The firing behavior was studied as a function of the mean and variance of the input current. Noise of a small amplitude can turn off the spiking for values of $\mu$ ranging from slightly smaller to significantly larger than ${\mu }_c$, and the number of spikes undergoes a minimum as a function of the noise level.Such a minimum has the opposite character to stochastic resonance and is called {\it inverse stochastic resonance}. Similar findings are obtained in the case of conductance-based noise, indicating that the phenomena are of a general nature. For long periods of observation, many 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 probabilities that noise shifts the process from the basin of attraction of a stable limit cycle to that of a stable rest state. These probabilities depend strongly on the values of $\mu$ and $\sigma$ and on the forms of the basins of attraction.

The observed effects of noise will be found in all systems with the same underlying dynamical structure.