In response to the reviewer's comment that "seems to be" does not sound scholarly and should be changed to "is": I believe that "seems to be" should be easily understood as scholarly, because it expresses the exact truth. I have not read a description of the intuition behind the word "unfolding" anywhere. I was expressing what seems (to me) likely to have been the idea behind the word. I suspect (but do not know for certain) that the word was introduced by Thom (in connection with singularity and catastrophe theory), and Thom's writing is notoriously unclear--he loves to express vague intuitions in French that is apparently difficult to translate. If anyone can provide me with the proper reference for the first use of the word (or a later explanation by the originator of the terminology) I would be happy to change "seems to be" to "is" (if I was right) or change the explanation (if I was not). In the meantime, the idea still seems to be what I said it seemed to be.
Reviewer's reaction: I did not mention scholarship, and it is not under discussion here. I mentioned encyclopedia, which I interpret as being about factual statements. The way you put it, you introduce unnecessary uncertainty in the article at a very early stage. Why not say: (This can be interpreted as ...) or something similar? If you want to stick to your sentence, then the scholarly thing to do would be to read the possible origins of the terminology and talk to the experts, but that to me does not seem to be worth the trouble at this stage.
Ok, I am willing to change the sentence to "(One may picture the various behaviors of the expanded system as being hidden or "folded up" when the parameters are set to zero.) I'll put this, or something like it, in my final revision.
The latest comments (by a new reviewer?) make worthwhile suggestions which I will consider as soon as I have time. The one saying that a certain matrix must be multiplied by a vector is, of course, correct and will be changed. Also I will certainly link to the TB article. I did not mean the ending to sound "down". In particular, the asymptotic method allows quick calculation of unfoldings, one given in the references having codimension 14. On the other hand, nothing has been done to make effective use of unfoldings with high codimension. As to examples to end with, I can certainly cite the zero-Hopf with references to Wiggins and Guckenheimer & Holmes. I thought of my article as being about the idea and computation of unfoldings, rather than the subsequent bifurcation analysis. If you have specific ideas, I would appreciate more suggestions here.
Reviewer's comments: I am not sure whether the author is still working or this or not - I received a notice that changes have been made, but there were still some vectors that were missing. I have added those - please check that this is what was intended by looking at the difference between the previous version. The reference I was thinking about is
title=Generic three-parameter families of planar vector elds, unfoldings of saddle, focus, and elliptic singularities with nilpotent linear parts, author=Dumortier, F. and Roussarie, R. and Sotomayor, J., journal=Lecture Notes in Mathematics, volume=1480, pages=1--164, year=1991
This may be somewhat specialized, but I thought it was a nice example of an unfolding that has, in fact, been used in practice.