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

Biol Cybern. 2008 Nov;99(4-5):319-34. doi: 10.1007/s00422-008-0267-4. Epub 2008 Nov 15.


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.

MeSH terms

  • Action Potentials / physiology
  • Models, Neurological*
  • Neurons / physiology*