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

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

Published:2019-12-10 Issue:13 Volume:29 Page:1950186
ISSN:0218-1274
Container-title:International Journal of Bifurcation and Chaos
language:en
Short-container-title:Int. J. Bifurcation Chaos

Author:

Bashkirtseva Irina¹,Ryashko Lev¹^ORCID

Affiliation:

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

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.

Funder

Russian Science Foundation

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modeling and Simulation,Engineering (miscellaneous)

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218127419501864

Reference34 articles.

1. In-phase and anti-phase synchronization in noisy Hodgkin–Huxley neurons

2. Noise-induced resonances in the Hindmarsh-Rose neuronal model

3. ANALYSIS OF STOCHASTIC CYCLES IN THE CHEN SYSTEM

4. Stochastic sensitivity analysis of noise-induced suppression of firing and giant variability of spiking in a Hodgkin-Huxley neuron model

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