Modeling the electrical activity of a neuron by a continuous and piecewise affine hybrid system

Jean-Guillaume Dumas (1) , Aude Rondepierre (1)

1 LMC - IMAG - Laboratoire de Modélisation et Calcul

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.

Domaines: Systèmes dynamiques [math.DS]

Jean-Guillaume Dumas, Aude Rondepierre. Modeling the electrical activity of a neuron by a continuous and piecewise affine hybrid system. Hybrid Systems: Computation and Control , Apr 2003, Prague, Czech Republic. pp.156-171, ⟨10.1007/3-540-36580-X_14⟩. ⟨hal-01807138⟩