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Dynamics and bifurcations of the adaptive exponential integrate-and-fire model. (English) Zbl 1161.92016
Summary: 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.

92C20 Neural biology
92C05 Biophysics
37N25 Dynamical systems in biology
34C60 Qualitative investigation and simulation of ordinary differential equation models
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