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

@inproceedings{Berglund2011MixedmodeOA,
  title={Mixed-mode oscillations and interspike interval statistics in the stochastic FitzHugh-Nagumo model},
  author={Nils Berglund and Damien Landon},
  year={2011}
}
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… CONTINUE READING
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