The Hodgkin-Huxley neuron model on the fast phase plane | Zendy

A William | Zendy; H Salas Alvaro | Zendy; Janeth Gonzalez Colorado Silvia | Zendy

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The Hodgkin-Huxley neuron model on the fast phase plane

Author(s) -

A William,

H Salas Alvaro,

Janeth Gonzalez Colorado Silvia

Publication year - 2013

Publication title -

international journal of the physical sciences

Language(s) - English

Resource type - Journals

ISSN - 1992-1950

DOI - 10.5897/ijps11.1334

Subject(s) - hodgkin–huxley model , phase portrait , biological neuron model , phase plane , plane (geometry) , ordinary differential equation , dynamical systems theory , mathematics , differential equation , statistical physics , artificial neural network , computer science , physics , mathematical analysis , artificial intelligence , geometry , neuroscience , nonlinear system , bifurcation , quantum mechanics , biology

In this paper, we showed a simplified version of the Hodgkin-Huxley neuron model, the so called fast plane-phase case. We first describe the circuit model of axon membrane with four parallel branches described by Hodgkin and Huxley and then we apply the Kirchhoff´s laws to obtain a system ordinary differential equations. We obtain numerical solutions to it with the aid of Mathematica. We also study this simplified model from the point of view of dynamical systems. With the aid of Maple we graph the phase portrait corresponding to the dynamical system associated to Hodgkin-Huxley model. At the end we interpret the results. Key words: Neuron model, Hodgkin-Huxley neuron model, cell membrane, ionic channel dynamics, fast phase plane, nullclines, mathematical.

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