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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.

The Hodgkin-Huxley neuron model on the fast phase plane