title: Origin of bursting through homoclinic spike adding in a neuron model.
abstract: The origin of spike adding in bursting activity is studied in a reduced model of the leech heart interneuron. We show that, as the activation kinetics of the slow potassium current are shifted towards depolarized membrane potential values, the bursting phase accommodates incrementally more spikes into the train. This phenomenon is attested to be caused by the homoclinic bifurcations of a saddle periodic orbit setting the threshold between the tonic spiking and quiescent phases of the bursting. The fundamentals of the mechanism are revealed through the analysis of a family of the onto Poincaré return mappings.
authors.affiliation: Department of Mathematics and Statistics, Georgia State University, Atlanta, GA 30303, USA.
authors.forename: Paul
authors.initials: P
authors.lastname: Channell
authors.forename: Gennady
authors.initials: G
authors.lastname: Cymbalyuk
authors.forename: Andrey
authors.initials: A
authors.lastname: Shilnikov
mesh_terms: D000465:Algorithms; D000818:Animals; D004594:Electrophysiology; D006321:Heart / Q000294:innervation*; D007395:Interneurons / Q000502:physiology*; D007865:Leeches / Q000502:physiology*; D008959:Models, Neurological; D015233:Models, Statistical; D009474:Neurons / Q000502:physiology*; D015221:Potassium Channels / Q000187:drug effects / Q000502:physiology
chemical_list: D015221:Potassium Channels