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Pré-Publication, Document De Travail Année : 2011

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

Résumé

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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Dates et versions

hal-00591089 , version 1 (06-05-2011)
hal-00591089 , version 2 (13-10-2011)
hal-00591089 , version 3 (13-10-2011)
hal-00591089 , version 4 (05-04-2012)

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  • HAL Id : hal-00591089 , version 2

Citer

Nils Berglund, Damien Landon. Mixed-mode oscillations and interspike interval statistics in the stochastic FitzHugh-Nagumo model. 2011. ⟨hal-00591089v2⟩
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