title: Neuron firing in driven nonlinear integrate-and-fire models.
abstract: Statistical properties of neuron firing are studied in the framework of a nonlinear leaky integrate-and-fire model that is driven by a slow periodic subthreshold signal. The firing events are characterized by first passage time densities. The experimentally better accessible interspike interval density generally depends on the sojourn times in a refractory state of the neuron. This aspect is not part of the integrate-and-fire model and must be modelled additionally. For a large class of refractory dynamics, a general expression for the interspike interval density is given and further evaluated for the two cases with an instantaneous resetting (i.e. no refractory state) and a refractory state possessing a deterministic lifetime. First passage time densities and interspike interval densities following from the proposed theory compare favorably with precise numerical simulations.
authors.affiliation: Institut für Physik, Universität Augsburg, D-86135 Augsburg, Germany.
authors.forename: Marcin
authors.initials: M
authors.lastname: Kostur
authors.forename: Michael
authors.initials: M
authors.lastname: Schindler
authors.forename: Peter
authors.initials: P
authors.lastname: Talkner
authors.forename: Peter
authors.initials: P
authors.lastname: Hänggi
mesh_terms: D000200:Action Potentials / Q000502:physiology*; D000465:Algorithms; D000818:Animals; D003198:Computer Simulation; D025802:Electric Capacitance; D004594:Electrophysiology; D006801:Humans; D008390:Markov Chains; D008959:Models, Neurological; D009431:Neural Conduction / Q000502:physiology*; D009474:Neurons / Q000502:physiology; D017711:Nonlinear Dynamics; D012032:Refractory Period, Electrophysiological / Q000502:physiology