title: Chaotic solutions in the quadratic integrate-and-fire neuron with adaptation.
abstract: The quadratic integrate-and-fire (QIF) model with adaptation is commonly used as an elementary neuronal model that reproduces the main characteristics of real neurons. In this paper, we introduce a QIF neuron with a nonlinear adaptive current. This model reproduces the neuron-computational features of real neurons and is analytically tractable. It is shown that under a constant current input chaotic firing is possible. In contrast to previous study the neuron is not sinusoidally forced. We show that the spike-triggered adaptation is a key parameter to understand how chaos is generated.
authors.affiliation: ECS, ENSEA, 6 Avenue du Ponçeau, 95014, Cergy-Pontoise Cedex, France, Gang.Zheng@ensea.fr.
authors.forename: Gang
authors.initials: G
authors.lastname: Zheng
authors.forename: Arnaud
authors.initials: A
authors.lastname: Tonnelier