Bona fide stochastic resonance and multimodality in the stochastic Hodgkin-Huxley neuron.

The phenomena of stochastic resonance (SR) has attracted much attention in the studies of the excitable systems, in particular, the nervous systems under noise. Recently, an alternative SR condition, called the bona fide SR, was proposed for the bistable system under noise, based on the notion of the residence time distribution. As the forcing frequency increases, there exists an optimal resonant frequency. We study the SR in a stochastic Hodgkin-Huxley neuron, which has an inherent natural frequency in addition to the stochastic time scale. We have observed two resonant conditions; one between periodic forcing and natural frequencies, and the other between the periodic forcing and the stochastic frequencies. These resonance conditions show the bona fide stochastic resonance with multimodality. For comparison, we have studied the bona fide SR in the stochastic FitzHugh-Nagumo neuron, where, the multimodality is not observed. The differences in the resonance structure of two neuron models are understood in terms of differences in the phase portraits.