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

by Jonathan Touboul, Romain Brette
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.
Reference:
Jonathan Touboul, Romain Brette, 2008.Dynamics and bifurcations of the adaptive exponential integrate-and-fire model, Biological cybernetics, volume 99.
Bibtex Entry:
@article{Touboul2008,
 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 Poincar{'e} 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.},
 author = {Touboul, Jonathan
and Brette, Romain},
 day = {15},
 doi = {10.1007/s00422-008-0267-4},
 issn = {1432-0770},
 journal = {Biological cybernetics},
 keyword = {Neurons},
 language = {eng},
 month = {Nov},
 number = {4-5},
 pages = {319--334},
 pmid = {19011921},
 title = {Dynamics and bifurcations of the adaptive exponential integrate-and-fire model.},
 volume = {99},
 year = {2008}
}