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

Jonathan Touboul 1, 2, * Romain Brette 1
* Corresponding author
1 ODYSSEE - Computer and biological vision
DI-ENS - Département d'informatique - ENS Paris, CRISAM - Inria Sophia Antipolis - Méditerranée , ENS-PSL - 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.
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https://hal.inria.fr/inria-00288734
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Submitted on : Wednesday, July 2, 2008 - 5:00:46 PM
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  • HAL Id : inria-00288734, version 4

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Jonathan Touboul, Romain Brette. Dynamics and bifurcations of the adaptive exponential integrate-and-fire model. [Research Report] RR-6563, INRIA. 2008. ⟨inria-00288734v4⟩

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