Analytical approach to the stochastic FitzHugh-Nagumo system and coherence resonance

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Abstract
We consider the FitzHugh-Nagumo system under the influence of white Gaussian noise in the excitable regime. We present an analytical approximation in the limit of fast activator time scale. Marginal probability densities of a reduced system and dynamical quantities such as the pulse rate are found and the mean interspike interval and its relative standard deviation are investigated. The latter quantities allow a quantitative description of the phenomenon of coherence resonance, as comparisons with simulations show.