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 nonlinear 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. © Springer-Verlag Berlin Heidelberg 2003.
CITATION STYLE
Dumas, J. G., & Rondepierre, A. (2003). Modeling the electrical activity of a neuron by a continuous and piecewise affine hybrid system. Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2623, 156–171. https://doi.org/10.1007/3-540-36580-x_14
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