Talk:Fold-Hopf bifurcation

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    I added the reference to Wittenberg and Holmes.



    John, I made a few cosmetic changes, mostly in punctuation and to format the references consistently. I am disappointed that you do not wish to refer to the Wittenberg-Holmes review. My only interest was to make this whole endevor maximally useful to users. The comment about 'wasting my time' was prompted by the fact that either you or Kuznetsov had not looked at all the changes I made last time round.

    If you accept the changes I made this time round I promise that I will not make any more.


    Edgar: I hope I have addressed your comments - no intent to waste your time. I changed the notation for omega (no subscripts now), delete the Wiggins reference, added a citation to Chmapneys and Kirk and added a reference to the Brusselator as an example of this bifurcation.



    Adding "Gavrilov-Guckenheimer" is OK with me, although very few people call it this way. Yu.K.

    I agree to include Gavrilov-Guckenheimer. I have heard this several times. I would also suggest that you add saddle-node/Hopf. This is used quite a lot in the literature (e.g. Vivien Kirk, Edgar Knobloch). In my view one of the things scholarpedia articles should do is to reflect the current accepted norms in terms of notation and nomenclature rather than correct historical anomolies.

    Which brings me to my main point (not really to do with this article, but generally the articles on dynamical systems). I think you should stick to calling a "Hopf bifurcation" a "Hopf bifurcation". I know Andronov-Hopf is historically more accurate, but Hopf bifurcation is now SO widely used not just in our dynamical systems community, that I think you should reflect that.

    So I would suggest you rename that page "Hopf bifurcation" and somewhere near the top you have a statement "also known as an Andronov-Hopf bifurcation".

    Similarly "saddle-node" is used very widely to mean "fold" (even though the invariant sets involved might not be saddles or nodes).

    Regards, Alan Champneys


    The following are comments by Edgar Knobloch:

    There is a large number of typos in the submitted version:

    please correct the following (and I will then have another go):

    2nd para: a branch of torus bifurcations

    3rd and 4th bullets: bifurcation curve; delete punctuation at the end of lines

    next para l.2: bifurcation, l.7 torus bifurcations, l.11 disappear

    reversal of time

    Next paragraph: l.1 formulas; l.2 cylindrical

    Equations: what is the r in all the equations between ZH.2 and ZH.3?

    You need to explain what <...> means. Remember that these articles are not only for experts. On the contrary!

    Other Cases: infinite-dimensional

    Ref 1: remove V. after Kirk

    Final comment: I think it would be good to explain that normal forms are not unique. For example, Wiggins uses a different normal form with additional nonlinear terms and the reader will rightly ask which normal should he/she should use (and does he/she need to know the coefficients!) So you should explain what you can get using your normal form and what can be obtained with 'other' normal forms.

    I think that you should also explain the different possible ways to unfold problems of this type.

    And a reference to something like the Holmes-Wittenberg Physica D review would be helpful to show the reader both the power of the normal form approach AND its shortcomings.

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