Preprint 6/2009

Inverse stochastic resonance in neuronal models: modulation and inhibition of rhythmic spiking by noise

Henry Tuckwell, Jürgen Jost, and Boris Gutkin

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Submission date: 16. Jan. 2009
Bibtex
Keywords and phrases: stochastic processes, Neural models

Abstract:
We investigated the effects of noise on the periodic firing activity of the Hodgkin-Huxley nonlinear system. With mean input current formula4 as a bifurcation parameter, an Andronov-Hopf bifurcation to repetitive spiking occurs at a critical value formula6 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 formula4 ranging from slightly smaller to significantly larger than formula10, 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 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 formula4 and formula14 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.

07.06.2018, 02:11