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

Jonathan Touboul (1) , Romain Brette (1)

1 ODYSSEE - Computer and biological vision

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.

Domaines: Algorithme et structure de données [cs.DS]; Imagerie médicale

Jonathan Touboul, Romain Brette. Dynamics and bifurcations of the adaptive exponential integrate-and-fire model.. Biological Cybernetics (Modeling), 2008, 99 (4-5), pp.319-34. ⟨10.1007/s00422-008-0267-4⟩. ⟨inria-00422701⟩