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} }