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Stochastic Sensitivity and Method of Principal Directions in Excitability Analysis of the Hodgkin–Huxley Model

Irina Bashkirtseva

Institute of Natural Sciences and Mathematics, Ural Federal University, Lenina, 51, Ekaterinburg 620000, Russia

E-mail Address: Irina.Bashkirtseva@urfu.ru

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and

Lev Ryashko

http://orcid.org/0000-0002-0817-3753

Institute of Natural Sciences and Mathematics, Ural Federal University, Lenina, 51, Ekaterinburg 620000, Russia

E-mail Address: Lev.Ryashko@urfu.ru

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https://doi.org/10.1142/S0218127419501864Cited by:10 (Source: Crossref)

Abstract

We study the probabilistic behavior of the Hodgkin–Huxley neuron model in the presence of random forcing of the external current parameter. The stochastic excitement in the zone of stable equilibria is illustrated by the statistics of interspike intervals and probabilistic distributions of mixed-mode oscillations. For the parametric analysis of this phenomenon, a constructive method for stochastic sensitivity and confidence ellipsoids is suggested. It is shown how to simplify this analysis using the principal direction approach. A constructive application of this technique is demonstrated by analyzing the stochastic excitement in the Hodgkin–Huxley model.

Keywords:

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