View source for Talk:Ermentrout-Kopell canonical model

This is an excellent draft.  I have the following suggestions for improvement:

1.  It would be good if Figure 1 were replaced by, or supplemented by, a 2-D diagram associated with a neural phase plane.  Right now, the derivation part is a bit confusing, because one doesn’t see how to connect this to anything neural.  Also, there is no mention that this is a bifurcation of a 2-D picture, so I was confused for a while what the stable manifold was doing in figure 1.  
Note the typo in “bifurcation”.  

2.  None of the references are currently in the draft.  It would be helpful to have references to Types I and II, all the models mentioned and the Izekevitch neuron.   Also, say where it was “suggested” that the PRC is a signature of neurons undergoing SNIC.

3.   The description of the derivation describes the formal procedure very well.  But it then took a lot of work to show that this was “kosher”.  It is not appropriate to go through all of that here, but perhaps it does make sense to at least hint that this was not obvious (remember: the draft with only the formal derivation first got rejected!) and send the reader to the original paper for the details.  

4. In the section on the noisy theta models, the resulting equation has a deterministic term 
(sigma^2 /2 sin theta) that is not in the first equation.  This is likely to confuse the reader.  Can it be explained?  

5.  A trivial aesthetic point: the “prime” is a raised comma, and looks funny.  If you can’t get this to be a real prime, use du/dt.    The * for u* is in a strange place.  

T<review>message to curators</review>hanks for doing this!
Nancy

Nice article

I would only add a couple of things:


1. In the stochastic version of the theta-neuron one should point out that if the noise variance is sufficiently small, then the middle term (the extra term in the drift) can be neglected giving the model previously used in Gutkin and Ermentrout '98.

2. Perhaps one should point out why use the theta-neuron instead of the QIF? I am thinking of the fact that the model is continuous during the spike (theta=pi) and the reset is near the rest. Hence there is no loss due to the rest at the spike time. This sometimes does make a difference in the QIF as pointed out earlier in Trocme et al. -- the PRC changes the skew as the reset value for the spike is changed.

Otherwise, nice ...