Very nice article! The history section adds a personal dimension that is engaging.
Note that the captions to figures 1 and 2 indicate that theta=1, but the form of the MG equation shown in Eq. 1 does not have the theta.
It is unclear to this reviewer what is meant by a need to examine return maps in the 'search for chaos' section. Embedding theorems suggest that delay maps retain the structure of the original attractor, and more recent results suggest what happens if the embedding is not done correctly. ?
Note a few very minor edits.
I don't see that anything has changed. Am I missing something?
If you don't want to address the return map question, at least remove the thetas in the figure captions.
Regarding the return map comment: please remember that this is an encyclopedia article, and as such it will have a certain permanency that may be misleading to future readers
OK, I figured out how to remove the thetas in the figure captions.
This is a nice article for what it is attempting to do. The Mackey-Glass equation has inspired a great deal of work in the pure mathematics community (equations of the form x'(t)=f(x(t),x(t-a)), however, and none of that work is mentioned. One of the lessons of that work is how hard it is to prove, in a mathematically rigorous way, various assertions which may seem reasonable on the basis of numerical studies. It would increase the utility of this article if some of that work were mentioned. It would also be helpful if the authors addressed the issue of how much of the work on the Mackey-Glass equation by Farmer, Ott and Yorke, etc. is mathematically rigorous. For example, rigorously proving existence of "chaos", even for simpler differential-delay equations, is highly non-trivial. I realize that the authors' interest is not particularly in describing or proving rigorous results here, but a few sentences could clarify the (rigorous) mathematical picture
see remarks by "Reviewer C".
The revised article seems fine. There are, however, some minor changes which should be made in the final four lines of the section "Relevance to Nonlinear Dynamics". Instead of "g(t-1)", the equation should have "g(x(t-1))". I am not even sure what is meant by the final sentence fragment in the section: "...such as 1 that contain both exponential decay and nonmonotonic delayed feedback delayed feedback (Rost and Wu, 2007)>" something seems wrong with the grammar.
This is a very nice article, and I believe it is well worth being put online. This is a very interesting story.
Two relatively minor remarks:
1. for some reason I do not understand the "ff" in "differential" on the first line was in a stange font in Firefox (on a Mac) when I accessed the page. This has now disappeared upon closing and reopening Firefox; 2. from a mathematican's point of view, chaotic dynamics has a technical meaning (in fact one of many possibilities...). I thought the introduction of the return map as suggested by Ruelle was quite nice, but mathematicans would, I believe, appreciate a footnote maybe or an aside remark that rigorously proving chaotic dynamics in the infinite-dimensional system is a highly nontrivial task (in fact, is there a full proof of chaos in this system for those parameter values, or only for similar "model" systems ? (eg piecewise something or other)).