Extending Power Series Methods for the Hodgkin-Huxley Equations, Including Sensitive Dependence

Authors

James S. Sochacki, James Madison UniversityFollow

Publication Date

11-30-2020

Keywords

Neuron Modeling, Hodgkin-Huxley Equations, Power Series, Sensitive Dependence

Disciplines

Computational Neuroscience | Mathematics | Neuroscience and Neurobiology | Science and Mathematics Education

Abstract

A neural cell or neuron is the basic building block of the brain and transmits information to other neurons. This paper demonstrates the complicated dynamics of the neuron through a numerical study of the Hodgkin-Huxley differential equations that model the ionic mechanisms of the neuron: slight changes in parameter values and inputted electrical impulses can lead to very different (unexpected) results. The methods and ideas developed for the ordinary differential equations are extended to partial differential equations for Hodgkin-Huxley networks of neurons in one, two and three dimensions.

Recommended Citation

Sochacki, James S. (2020) "Extending Power Series Methods for the Hodgkin-Huxley Equations, Including Sensitive Dependence," CODEE Journal: Vol. 13, Article 2.
Available at: https://scholarship.claremont.edu/codee/vol13/iss1/2

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