Reviewer A 2nd Version
I'm happy with the corrections.
The only needed change now is to correct
adequat --> adequate.
This is a nice article.
I suggest rewriting the phrase
"...the minimal embedding dimension for a (continuous) system is 4."
"...the minimal dimension for a (continuous) hyperchaotic system is 4."
The need for hyperchaotic is obvious. As for the omission of the word "embedding", I believe that it could cause some confusion with the "minimum embedding dimension" in the sense of Takens' theorem.
It would be nice to indicate the Poincare' section used to produce Fig. 2. In that respect, I would suggest to rethink the phrase:
"its structure reveals a large thickness and the lack of any obvious monotonic branches."
Could it be that the lack of monotonic branches be related to the system (and therefore the Poincare section) dimension (now 4D)? If you simulate the system with a set of parameters that yield chaos (just one positive Lyapunov exponent) and take the same Poincare section and plot the first return map, what do you get? Obvious monotinic branches? If so, then you may stress your assertion. Otherwise you will want to rephrase it.
It is not clear from the text if the folded towel map is due to Rossler 1979.
As for the 9D model, in the text the authors use r and in Fig. 6 they use R.
"The transition from chaos to hyperchaos is observed around r=43.3 where a second positive Lyapunov exponent appears"
The second Lyaponov exponent becomes positive at r aprox. 43.3. "Appears" is not adequate here, it may convey the wrong impression.
"by Kapitaniak et al for driven systems and, consequently, is still to characterize."
I didn't understand. What is still to characterize?
The section: Experimental hyperchaotic behaviours is both interesting and confusing. This section should be rewritten. In doing so, I suggest the authors to make a clear distinction (at the moment this is not the case) between hyperchaos and the increase of the system dimension. It is perfectly possible to increase the dimension of a system without becoming hyperchaotic. Also, a system may become hyperchaotic or *more strongly hyperchaotic* without needing to increase the dimension.
Please use either behavior or behaviour.
"Very few experimental (hyperchaotic) behavior have been identified. This (possibly) results from..."
I would add the words in parentheses. Please consider.
Lyapunovexponent -> Lyapunov exponent
For the sake of completion, I would suggest the authors to provide the two positive Lyapunov exponents for the first three systems presented: 4D Rossler, folded towel and generalized Henon.
This is a very nice article. It needs only a little editing before being mounted on the scholarpedia website.
Figs. 1 and 3 obscure the equations to their right. Some e-magic should be performed to solve this problem.
Figs. 1 & 2 are specifically called out in the text. Figs. 3 - 6 qre not. The last four should be explicitly pointed to in the text from a sentence that explains what these figures show.
In Sec. 1: lools -> looks; conjugaison - conjugation
Sec. 3: proposed in 1998 -> proposed by Reiterer in 1998
a should be italics everywhere, in particular in the line below the equations. Also what is a? the ratio of the cell height to edge length?
still to characterize -> is still not completely understood
Sec. 4: experimental behavior -> experimental hyperchaotic systems
rewrite last sentence to something like: In the 9D model observability is significantly reduced in the hyperchaotic regime when the first postiive Lyapunov exponent is an order of magnitude larger than the second positive Lyapunov exponent.
Sec. 5: include a reference to the zork described in the first paragraph (if published), to Baier and Sahle, and to Hudson and Rossler. Differentiability is misspelled. If purposely, it should be more poetically tuned to the one on the next line, which seems to be Weierstrassicity (??).
paly -> play