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

被引：0
作者：
Jonathan Touboul
Romain Brette
机构：
[1] Ecole Normale Supérieure,Département d’Informatique, Projet Odyssée
来源：
Biological Cybernetics | 2008年 / 99卷
关键词：
Integrate-and-fire; Spiking neuron models; Dynamical systems; Bifurcations; Chaos;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
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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页码：319 / 334
页数：15
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[1]  
Angelino E(2007)Excitability constraints on voltage-gated sodium channels PLoS Comput Biol 3 1751-1760
[2]  
Brenner MP(2008)Dynamic IV curves are reliable predictors of naturalistic pyramidal-neuron voltage traces J Neurophysiol 99 656-56
[3]  
Badel L(2004)Dynamics of one-dimensional spiking neuron models J Math Biol 48 38-3642
[4]  
Lefort S(2005)Adaptive exponential integrate-and-fire model as an effective description of neuronal activity J Neurophysiol 94 3637-1673
[5]  
Brette R(2007)Predicting neuronal activity with simple models of the threshold type: Adaptive Exponential Integrate-and-Fire model with two compartments Neurocomputing 70 1668-1070
[6]  
Petersen C(2003)How spike generation mechanisms determine the neuronal response to fluctuating inputs J Neurosci 23 11,628-424
[7]  
Gerstner W(2004)Which model to use for cortical spiking neurons? IEEE Trans Neural Netw 15 1063-635
[8]  
Richardson M(2008)A benchmark test for a quantitative assessment of simple neuron models J Neurosci Meth 169 417-807
[9]  
Brette R(1907)Recherches quantitatives sur l’excitation électrique des nerfs traitée comme une polarisation J Physiol Pathol Gen 9 620-2554
[10]  
Brette R(2004)Interneurons of the neocortical inhibitory system Nat Rev Neurosci 5 793-1079
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