×

zbMATH — the first resource for mathematics

Spiking dynamics of bidimensional integrate-and-fire neurons. (English) Zbl 1204.37019
The original results of the authors refer to spiking neuron models as hybrid dynamical systems combining ordinary differential equations and discrete resets. It is proved that the spike patterns are related to orbits under a discrete adaptation map whose dynamics is based on bifurcations. Regular spiking corresponds to fixed points of the adaptation map, while bursting corresponds to periodic orbits. The authors prove that their models undergo a transition to chaos via a cascade of period adding bifurcations. Also, they discuss about the physiological relevance of the original results with regard to electrophysiological classes.

MSC:
37C10 Dynamics induced by flows and semiflows
37B10 Symbolic dynamics
Software:
MATCONT
PDF BibTeX XML Cite
Full Text: DOI