title: Dynamical phase transitions in periodically driven model neurons.
abstract: Transitions between dynamical states in integrate-and-fire neuron models with periodic stimuli result from tangent or discontinuous bifurcations of a return map. We study their characteristic scaling laws and show that discontinuous bifurcations exhibit a kind of phase transition intermediate between continuous and first order. In the model-independent spirit of our analysis we show that a six-dimensional (6D) gating variable model with an attracting limit cycle has similar phase transitions, governed by a 1D return map. This reduction to 1D map dynamics should extend to real neurons in a periodic current clamp setting.
authors.affiliation: Department of Physics, Boston College, Chestnut Hill, Massachusetts 02467, USA.
authors.forename: Jan R
authors.initials: JR
authors.lastname: Engelbrecht
authors.forename: Renato
authors.initials: R
authors.lastname: Mirollo
mesh_terms: D000200:Action Potentials / Q000502:physiology*; D000818:Animals; D001683:Biological Clocks / Q000502:physiology*; D003198:Computer Simulation; D006801:Humans; D008959:Models, Neurological; D009415:Nerve Net / Q000502:physiology*; D009474:Neurons / Q000502:physiology*; D010507:Periodicity