title: Continuum of weakly coupled oscillatory McKean neurons.
abstract: The McKean model of a neuron possesses a one-dimensional fast voltagelike variable and a slow recovery variable. A recent geometric analysis of the singularly perturbed system has allowed an explicit construction of its phase response curve [S. Coombes, Physica D 160, 173 (2001)]. Here we use tools from coupled oscillator theory to study weakly coupled networks of McKean neurons. Using numerical techniques, we show that the McKean system has traveling wave phase-locked solutions consistent with that of a network of more biophysically detailed Hodgkin-Huxley neurons.
authors.affiliation: Department of Mathematical Sciences, Loughborough University, Leicestershire, LE11 3TU, United Kingdom. M.G.Denman-Johnson@lboro.ac.uk
authors.forename: M
authors.initials: M
authors.lastname: Denman-Johnson
authors.forename: S
authors.initials: S
authors.lastname: Coombes
mesh_terms: D000818:Animals; D004594:Electrophysiology / Q000379:methods*; D005583:Fourier Analysis; D006801:Humans; D008959:Models, Neurological; D015233:Models, Statistical; D008962:Models, Theoretical; D009474:Neurons / Q000473:pathology / Q000502:physiology*; D009991:Oscillometry; D013569:Synapses / Q000502:physiology