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Reports (Research Report) Year : 2008

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

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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Dates and versions

inria-00288734 , version 1 (18-06-2008)
inria-00288734 , version 2 (19-06-2008)
inria-00288734 , version 3 (19-06-2008)
inria-00288734 , version 4 (02-07-2008)

Identifiers

  • HAL Id : inria-00288734 , version 4

Cite

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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