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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.
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https://hal.archives-ouvertes.fr/hal-00591089
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Submitted on : Thursday, April 5, 2012 - 5:09:33 PM
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Nils Berglund, Damien Landon. Mixed-mode oscillations and interspike interval statistics in the stochastic FitzHugh-Nagumo model. Nonlinearity, IOP Publishing, 2012, 25 (8), pp.2303-2335. ⟨10.1088/0951-7715/25/8/2303⟩. ⟨hal-00591089v4⟩

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