Dynamics and bifurcations of the adaptive exponential integrate-and-fire model.

Jonathan Touboul 1 Romain Brette 1
1 ODYSSEE - Computer and biological vision
DI-ENS - Département d'informatique de l'École normale supérieure, CRISAM - Inria Sophia Antipolis - Méditerranée , ENS Paris - École normale supérieure - Paris, Inria Paris-Rocquencourt, ENPC - École des Ponts ParisTech
Abstract : Recently, several two-dimensional spiking neuron models have been introduced, with the aim of reproducing the diversity of electrophysiological features displayed by real neurons while keeping a simple model, for simulation and analysis purposes. Among these models, the adaptive integrate-and-fire model is physiologically relevant in that its parameters can be easily related to physiological quantities. The interaction of the differential equations with the reset results in a rich and complex dynamical structure. We relate the subthreshold features of the model to the dynamical properties of the differential system and the spike patterns to the properties of a Poincaré map defined by the sequence of spikes. We find a complex bifurcation structure which has a direct interpretation in terms of spike trains. For some parameter values, spike patterns are chaotic.
Type de document :
Article dans une revue
Biological Cybernetics (Modeling), Springer Verlag, 2008, 99 (4-5), pp.319-34. 〈10.1007/s00422-008-0267-4〉
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Contributeur : Alain Monteil <>
Soumis le : jeudi 8 octobre 2009 - 12:23:22
Dernière modification le : vendredi 25 mai 2018 - 12:02:04

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Jonathan Touboul, Romain Brette. Dynamics and bifurcations of the adaptive exponential integrate-and-fire model.. Biological Cybernetics (Modeling), Springer Verlag, 2008, 99 (4-5), pp.319-34. 〈10.1007/s00422-008-0267-4〉. 〈inria-00422701〉

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