View source for Talk:Hyperchaos

==Reviewer A==

This is a nice article.

I suggest rewriting the phrase

"...the minimal embedding dimension for a (continuous) system is 4."

as

"...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.