Analysis of excitability for the FitzHugh-Nagumo model via a stochastic sensitivity function technique

We study excitability phenomena for the stochastically forced FitzHugh-Nagumo system modeling a neural activity. Noise-induced changes in the dynamics of this model can be explained by the high stochastic sensitivity of its attractors. Computational methods based on the stochastic sensitivity functions technique are suggested for the analysis of these attractors. Our method allows us to construct confidence ellipses and estimate a threshold value of a noise intensity corresponding to the neuron excitement. On the basis of the proposed technique, a supersensitive limit cycle is found for the FitzHugh-Nagumo model.