Aperiodic stochastic resonance with correlated noise

Abstract

We examine the influence of the noise correlation on aperiodic stochastic resonance. To this end, we compute the discharge rate of a FitzHugh-Nagumo neuron model in response to a slow sub-threshold aperiodic input in the presence of additive correlated noise. Aperiodic stochastic resonance is observed for each level of noise correlation; i.e., there exists a noise amplitude that maximizes the covariance between the input signal and the model's discharge rate. Both the maximal covariance and the optimal noise level depend on the noise correlation. The former remains almost constant for low noise correlations, and steadily decreases at larger correlations. The latter displays a U-shaped curve when plotted against the noise correlation, indicating that aperiodic stochastic resonance occurs at lower noise amplitudes for an appropriate range of noise correlation. We show that the results are consistent with the evaluation of the discharge rate of the model through a quasistatic assumption. Our results suggest that the interplay of the noise correlation with the time scales of the neuron model can lead to an improvement of the aperiodic stochastic resonance effect, in that for an appropriate level of correlation maximal covariance can be attained with lower noise amplitude.