Modeling the Electrical Activity of a Neuron by a Continuous and Piecewise Affine Hybrid System

A hybrid system is proposed to model the electrical potential emitted by a neuron as a response to an externally applied DC current. Experimentally, Hodgkin and Huxley built a four-dimensional and non-linear dynamical system to simulate this activity. Our idea is to use a new continuous and piecewise affine approximation as a hybrid model of the Hodgkin-Huxley dynamic. Our new model reproduces the Hodgkin-Huxley features with good accuracy (e.g. including the fact that the incoming current intensity is a bifurcation parameter), and, moreover, still allows an analytic computation of its solutions.

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