View source for Phase response curve

==Classification of PRCs by Bifurcation Structure==

Hansel et al. (1995) identified two types of neural phase resetting curves:
* in Type I, the phase is only advanced by a small depolarization produced by excitatory postsynaptic potentials, whereas 
* in Type II either an advance or delay could be produced depending upon the timing of the perturbation. 
A small hyperpolarization similarly produces only delays in Type I PRCs but can produce either an advance or delay in Type II. Ermentrout (1996) showed that for the infinitesimal PRC this classification of phase response curves is closely related to the classification of [[Excitability|excitable membranes]] (Hodgkin, 1948). Excitable membranes can
undergo a transition from quiescence to repetitive firing of action
potentials in two ways as the applied depolarizing currents is increased.
* Type I excitable membranes can fire arbitrarily slowly near the onset of firing. 
* Type II excitable membranes have an abrupt onset of repetitive firing at a threshold frequency, and cannot be induced to fire at any frequency below the threshold frequency. 
Type I membrane excitability is exhibited by models near a [[saddle-node on invariant circle]] [[bifurcation]], and Type II near a [[Andronov-Hopf bifurcation]] (Rinzel and Ermentrout, 1989). Ermentrout's conclusion was that Type I resetting is associated with Type I excitability and Type II resetting with Type II excitability. Since an abrupt onset of firing may also be observed in the case of a [[saddle-node bifurcation]] away from the limit cycle (Izhikevich 2007), it may be more accurate to say that Type I resetting is associated with an integrator and Type II with a resonator.