Positive role of fractional Gaussian noise in FitzHugh–Nagumo neuron model - ScienceDirect
Fig. 1. Simulation of fGn with different values of Hurst parameter. When H = 0.3 < 0.5 , the process is anti-persistent, H = 0.5 , the process is Gaussian white noise, the sample is independent and H = 0.6 > 0.5 , H = 0.9 > 0.5 , the process is persistent. The Hurst parameter is larger, the correlation is stronger. Definition 1 Lemma 1 Theorem 1 Theorem 2 Proof of Theorem 1 Proof of Theorem 2 Fig. 2. Mutual information versus fGn noise variance as given by Eq. (39) for the FHN neuron model with 𝜀 = 0.001 , 𝑎 = 0.25 , 𝑏 = 0.08 , 𝐶 𝑇 = − 5 12 3 + 0.08 . The values of Hurst parameter are H=0.7, H=0.62 respectively, and the input signal are 𝑠 1 = − 0.05 , 𝑠 2 = 0.03 in this diagram. As the fGn intensity changes, the mutual information of the FHN neuron model takes the unimodal form. Fig. 3. Mutual information versus fGn noise variance as given by Eq. (39) for the FHN neuron model with 𝜀 = 0.001 , 𝑎 = 0.25 , 𝑏 = 0.08 , 𝐶 𝑇 = − 5 12 3 + 0.08 . The values of Hurs