Positive role of fractional Gaussian noise in FitzHugh–Nagumo neuron model

Determining the complex mechanisms of process information in the neural activity is found to be especially challenging. The noise with a 1/f power spectrum has been observed in nervous system, but its functional significance in the neuron activity remains unclear. Persistent effort has been made to determine the factors for efficient processing of information and for promoting the mutual information between stimulus and spike train output. Establishing the Fitzhugh–Nagumo (FHN) model coupling fractional Gaussian noise (fGn) as a special form of stochastic differential equation, our study is to certify the stochastic resonance (SR) effect in the process of neuron activity. We proved that the nonmonotonic SR effect about FHN neuron model driven by fGn occurred under the sufficient conditions based on the principle of forbidden interval. The simulated results show that appropriate intensity of fGn can enhance the increase of the mutual information. Compared with the Hurst parameters of fGn, the increase is more dependent on the noise intensity of fGn.