title: Transition between tonic spiking and bursting in a neuron model via the blue-sky catastrophe.
abstract: We study a continuous and reversible transition between periodic tonic spiking and bursting activities in a neuron model. It is described as the blue-sky catastrophe, which is a homoclinic bifurcation of a saddle-node periodic orbit of codimension one. This transition constitutes a biophysically plausible mechanism for the regulation of burst duration that increases with no bound like 1/square root alpha-alpha0 as the transition value alpha0 is approached.
authors.affiliation: Department of Mathematics and Statistics, Georgia State University, Atlanta, Georgia 30303, USA.
authors.forename: Andrey
authors.initials: A
authors.lastname: Shilnikov
authors.forename: Gennady
authors.initials: G
authors.lastname: Cymbalyuk
mesh_terms: D000200:Action Potentials / Q000502:physiology*; D000818:Animals; D001683:Biological Clocks / Q000502:physiology*; D003198:Computer Simulation; D006801:Humans; D008959:Models, Neurological; D009473:Neuronal Plasticity / Q000502:physiology*; D009474:Neurons / Q000502:physiology*; D017711:Nonlinear Dynamics