title: Ionic channel density of excitable membranes can act a bifurcation parameter.
abstract: As the maximal K+-conductance (or K+-channel density) of the Hodgkin-Huxley equations is reduced, the stable resting membrane potential bifurcates at a subcritical Hopf bifurcation into small amplitude unstable oscillations. These small amplitude solutions jump to large amplitude periodic solutions that correspond to a repetitive discharge of action potentials. Thus the specific channel density can act as a bifurcation parameter, and can control the excitability and autorhythmicity of excitable membranes.
mesh_terms: D000200:Action Potentials; D000818:Animals; D007473:Ion Channels / Q000502:physiology*; D007700:Kinetics; D008433:Mathematics; D008564:Membrane Potentials; D008954:Models, Biological; D011188:Potassium / Q000378:metabolism
chemical_list: D007473:Ion Channels; D011188:Potassium