Mixed-mode oscillations and interspike interval statistics in the stochastic FitzHugh-Nagumo model

Abstract

We study the stochastic FitzHugh-Nagumo equations, modelling the dynamics of neuronal action potentials, in parameter regimes characterised by mixed-mode oscillations. The interspike time interval is related to the random number of small-amplitude oscillations separating consecutive spikes. We prove that this number has an asymptotically geometric distribution, whose parameter is related to the principal eigenvalue of a substochastic Markov chain. We provide rigorous bounds on this eigenvalue in the small-noise regime, and derive an approximation of its dependence on the system's parameters for a large range of noise intensities. This yields a precise description of the probability distribution of observed mixed-mode patterns and interspike intervals.

36 pages

References in corpus (2)

• Hunting French Ducks in a Noisy Environment
• Mixed-Mode Oscillations in a Stochastic, Piecewise-Linear System

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