Talk:Hidden attractor

Unintelligble lede
I have just reverted an IP who tried to remove the context template. The issue should be dealt with before the template is removed. The lede of any article should be understandable by a general reader, even if the article later delves into technicalities. The first paragraph of the lede should clearly define its subject. It currently says:


 * From a computational point of view, in nonlinear dynamical systems periodic oscillations and chaotic attractors (a neighborhood of which is their attraction domain) can be regarded as self-excited attractors or hidden attractors.

This is a terrible lede, no one could posibly believe that it is understandable to a general readership. I am not even convinced that it succeeds in defining the term.  Spinning Spark  08:40, 13 November 2012 (UTC)


 * IMHO it is understandable and useful (this year I will get B.Sc. in Physics!) — Preceding unsigned comment added by Kuznetsov N.V. (talk • contribs) 21:40, 23 November 2012 (UTC)
 * The point is it should be understandable to a general reader. That is a reader who does not have B.Sc Physics.  Thanks for creating this article, it is a great subject to have on Wikipedia, but the language has big problems.  It completely fails to even define the term.  The title phrase is not even mentioned anywhere in the lede, let alone the first paragraph.  WP:LEAD asks for it to be in the first sentence as the sentence subject, preferably at the beginning.  After failing to do this it just gets worse, I am not even convinced it is right if read literally.  Spinning  Spark  22:58, 23 November 2012 (UTC)

Attractors, in addition to being important mathematically, are one of those rare math entities capable of fascinating a lay readership. High importance. This article is SLIGHTLY accessible to a general reader because the writing is logically consistent. However, in order to be truly instructive to a lay reader the article needs more basic instruction, more definition of terms and more available links. Thanks to the author, please develop further. 97.125.81.215 (talk) 18:54, 10 March 2013 (UTC)


 * I may suggest the following intro. In nonlinear dynamics, classification of attractors as being hidden or self-excited reflects the difficulties in numerical search for the local attractors in the phase space and the determination of necessary and sufficient conditions for the global convergence to the equilibrium points. Study of limiting behavior in dynamical system is focused on finding all possible local attractors in the phase space of the system. Trivial attractors, i.e.  stable equilibrium points, can be easily found analytically or numerically, while the search of  periodic and  chaotic attractors can turn out to be a challenging problem. For numerical localization of an attractor in the phase space, one needs to choose an initial point in  attractor’s basin of attraction and observe how the trajectory, starting from this initial point, after a transient process visualizes the attractor. nk (talk) 22:07, 15 March 2019 (UTC)

Needs secondary sources
This is an interesting subject, but all the sources appear to be WP:primary sources; (recent) research papers in scientific journals, by the same few authors: you, Leonov and Vagaitsev. Wikipedia requires primary sources to be backed up by secondary sources; survey articles or textbooks on the subject (WP:PSTS). Are there any? WP is not really the place to present research that has yet to be accepted.

Secondly, the fact that this page was started and largely written by the author of the only papers on the subject raises WP:conflict of interest issues. I respect your academic credentials and I'm sure your motives are pure. However, you can see that the lack of any other sources besides your own papers could give the appearance that "hidden oscillation" is a concept you are pushing to advance your own academic career. Adding sources by other authors would resolve any doubts about your motivation. -- Chetvorno TALK 18:31, 17 April 2017 (UTC)


 * Unless secondary sources from other authors besides Kuznetsov, Leonov, and Vagaitsev can be found, per WP:PSTS and WP:NEO I am going to merge this article into Oscillation. -- Chetvorno TALK 16:57, 24 May 2017 (UTC)


 * Hi, Chetvorno, I unwatched this page years ago as a hopeless case. As I said all those years ago, the article does not clearly define its topic.  This is far from my area of expertise, but I think there is a notable topic here, however, the page may be at the wrong title.  "Hidden oscillation" is a term widely used in control systems, has been studied for many years, and is certainly worthy of an article.  My understandin of hidden oscillation is an oscillation that is not apparent from the outputs of the system.  However, I'm not sure that this page is actually about hidden oscillation in this general sense.  The term is not bolded in the lead or defined anywhere.  The two terms that are bolded are "hidden attractor" and "self-excited attractor".  I'm guessing that the hidden oscillations occur in hidden attractors and not in self-excited attractors, but nowhere is this explained or clarified on the page.  Are hidden oscillations always associated with attractors?  Is a hidden oscillation always associated with a hidden attractor?  In other words, what is the connection between these things?  The attractor article might be a better merge target, but best of luck merging anywhere without a clear understanding of what we are discussing.  A search of gbooks readily shows that "hidden attractor" is a widely discussed concept and perhaps we would be better having an article at that title.  A gbooks search for "hidden oscillation" on the other hand mainly returns discussions of hidden oscillations due to sampling rates, something that is not discussed on this page at all. So in summary, there are plenty of secondary sources, but relating them to this article as it exists now is problematic. SpinningSpark 22:45, 24 May 2017 (UTC)


 * I agree that it is better to rename this article to “hidden attractor”, since “hidden oscillation” has too many other meanings. In general, an oscillation in dynamical system is just a nonstationary trajectory and is not necessary an attractor. But I do not know how to rename an article in wiki and keep the refs. I can also rewrite the text to add more rigorous mathematical definitions and revise the references list to make it more representative (e.g. a comprehensive survey was recetly pulished in one of the leading journals - Physics Report, and several books). nk (talk) 19:59, 21 March 2018 (UTC)
 * Renaming is easy, just use the "move" function, which is under the "More" tab at the top of the page. That's in the standard skin, if you are using something older "move" has probably got a tab of its own.  I don't know what you mean by "keep the refs".  Why do you think they would be lost? SpinningSpark 00:23, 22 March 2018 (UTC)
 * Thanks for the "move". But what will happen with refs "hidden oscillation" in other wiki articles?nk (talk) 09:09, 23 March 2018 (UTC)
 * They will get redirected. The standard move leaves a redirect behind at the original page. You can review those links by clicking "what links here" in the tools menu on the page.  If you wish, you can manually retarget them to the new page (or somewhere else if the link was inappropriate - quite possible given the multiple meanings of the current title). SpinningSpark 17:38, 23 March 2018 (UTC)


 * As the secondary sources and surveys I may suggest to consider the following papers. Comprehensive survey published in one of the leading journal by scientists from four different countries: D. Dudkowski, S. Jafari, T. Kapitaniak, N. V. Kuznetsov, G. A. Leonov, A. Prasad, Hidden attractors in dynamical systems, Physics Reports (A Review Section of Physics Letters), 637, 2016, pp. 1-50 (http://dx.doi.org/10.1016/j.physrep.2016.05.002). Two papers co-authored by well-known experts in dynamical systems and chaos Leon O. Chua and Chen Guanrong: N.V. Stankevich, N.V. Kuznetsov, G.A. Leonov, L. Chua, Scenario of the birth of hidden attractors in the Chua circuit, International Journal of Bifurcation and Chaos, 27(12), 2017, art. num. 1730038 (https://doi.org/10.1142/S0218127417300385), G. Chen, N.V. Kuznetsov, G.A. Leonov, T.N. Mokaev, Hidden attractors on one path: Glukhovsky-Dolzhansky, Lorenz, and Rabinovich systems, International Journal of Bifurcation and Chaos, 27(8), 2017 art. num. 1750115 (http://dx.doi.org/10.1142/80218127417501152). Also there are two recent open access surveys: Leonov G.A., Kuznetsov N.V., Mokaev T.N., Homoclinic orbits, and self-excited and hidden attractors in a Lorenz-like system describing convective fluid motion, European Physical Journal Special Topics, 224, 2015, pp. 1421-1458 (http://dx.doi.org/10.1140/epjst/e2015-02470-3) and N.V. Kuznetsov, G.A. Leonov, T.N. Mokaev, A. Prasad, M.D. Shrimali, Finite-time Lyapunov dimension and hidden attractor of the Rabinovich system, Nonlinear Dynamics, 92(2), 2018, 267-285 (https://doi.org/10.1007/s11071-018-4054-z) nk (talk) 22:34, 15 March 2019 (UTC)
 * It seems there is a typo in http://dx.doi.org/10.1142/80218127417501152. The correct one is https://doi.org/10.1142/S0218127417501152 KudryashovaLenaPhDMath (talk) 21:23, 20 March 2019 (UTC)

Revision of the article can be found here: User:Kuznetsov_N.V./sandbox. nk (talk) 14:17, 24 March 2019 (UTC)
 * I have updated text and refs here and deleted "refimprove science". nk (talk) 12:36, 5 April 2019 (UTC)


 * I'm sorry but you have not addressed the problem at all. Wikipedia is not a scientific journal; it requires all content be supported by citations from WP:secondary sources, textbooks and survey articles (WP:PSTS).  All the citations in this article are to WP:primary sources, scientific papers.  "A primary source may be used on Wikipedia only to make straightforward, descriptive statements of facts that can be verified by any educated person with access to the primary source but without further, specialized knowledge. Any interpretation of primary source material requires a reliable secondary source for that interpretation."(WP:PSTS)  The use of primary sources here goes far beyond this.


 * Second, this page has a huge WP:conflict of interest problem; it reads like Mr. Kuznetsov's private shrine. All the papers cited have Kuznetsov and Leonov as authors, one of the 2 books in the 'Books' section is by him, and both of the 'Selected lectures' are by him.  There is even an irrelevant image of an award given to Mr. Kuznetsov.  It seems as if Mr. Kuznetsov is trying to use this article either for personal promotion of his career, or for promotion of his classification system of "hidden attractors", which would benefit him.  That is WP:COI, WP:CITESPAM.


 * This subject is at least 11 years old. If, as Ms. Kudryashova says below, "Nowadays there is a number of papers by scientists from different countries in various well-known journals" on this subject, then cite them. There has been enough time for "hidden attractors" to be included in textbooks and surveys, if it is a concept important enough to have an article.  I think the page should be cut back to a stub until independent secondary sources are provided. --Chetvorno<i style="color: Purple;">TALK</i> 23:37, 21 December 2022 (UTC)

Templates
It is rather typical situation in the mathematical theory of chaos when a new term looks like a strange neologism, see e.g. blue sky catastrophe, pitchfork bifurcation, strange attractor and many others, including discussed term hidden attractor. Remark, that all the above terms have rigorous mathematical definitions. The “hidden attractor” is a mathematical notion having rigorous mathematical stipulative definition, and this definition has not been disproved by showing a logical contradiction during peer-review process in reputable journals (see, e.g. Hidden_attractor). The important question is whether such new notion (and its mathematical definition) will be accepted and widely used by specialists.

The notions of “hidden attractor” and “self-excited attractor”, and “classification of attractors as being self-excited or hidden” were introduced by G.A. Leonov and N.V. Kuznetsov about 10 years ago. Nowadays there is a number of papers by scientists from different countries in various well-known journals where the concept of hidden attractors and Leonov-Kuznetsov’s classification are used (see https://scholar.google.com/scholar?start=0&q=hidden+attractor), and even there is a number of papers where “hidden attractor” is used in the title of paper (see https://scholar.google.com/scholar?as_sdt=0%2C5&q=allintitle%3A+hidden+attractor+OR+self-excited+attractor).

For example, in the paper https://doi.org/10.1016/j.matcom.2014.01.001 “A new finding of the existence of hidden hyperchaotic attractors with no equilibria” it is written: A rigorous mathematical definition of a hidden attractor was first suggested by Leonov and Kuznetsov and Hidden attractors are important in engineering applications because they allow unexpected and potentially disastrous responses to perturbations in a structure like a bridge or an airplane wing. In the paper http://dx.doi.org/10.1142/S0218127417300373 by Clint Sprott and William G. Hoover it is written: The innermost limit cycle is self-excited since it can be found by starting with an initial condition in the neighborhood of the equilibrium at the origin, but the others are hidden [Leonov & Kuznetsov, 2013] and require a careful selection of initial conditions. In the paper http://dx.doi.org/10.1142/S0218127416300391 “Hidden bifurcations in the multispiral Chua attractor” by Tidjani Menacer, Rene Lozi and Leon O. Chua it is written: Recently a new concept concerning the classification of attractors has been introduced: periodic or chaotic attractors belong either to the class of self-excited attractors or to the class of hidden attractors [Leonov et al., 2011; Leonov & Kuznetsov, 2011] and This method is based on the core idea of the genuine Leonov and Kuznetsov method for searching hidden attractors.

Remark, that the concept of self-excited attractors has roots in the works of Aleksandr Andronov and Leonid Mandelstam (see, e.g. wiki article self-oscillation and survey by A. Jenkins “Self-oscillation”, Physics Reports, 525(2), 2013), and Heinrich Barkhausen (he used term Selbsterregte Schwingungen in German language). The epithet hidden may reflect that the attractor is hidden somewhere in the phase space and cannot be seen in standard engineering experiments and numerical simulation, where initial data belongs to vicinity of stationary points. This was the reason that such hidden chaotic attractors for a long time had been remained hidden from scientists. Until 2009 year when the first hidden chaotic attractor was described by N. Kuznetsov for the Chua circuit, for which hundreds of various self-excited attractors had been discovered before (see, e.g. Bilotta, E., Pantano, P., Gallery of Chua Attractors, World Scientific, 2008). At the same time, it is hidden attractors that often lead to incorrect operation of technical devices (see, e.g., problems of synchronization of two Chua circuits in the presence of hidden attractors). In contrast to the property strange (strange attractor), which characterize the attractor itself — it has fractional dimension, the property hidden and classification of being hidden or self-excited reflect the difficulties of revealing attractors and obtaining necessary & sufficient stability conditions, rather than characterize the attractor itself. Remark, also that not every type of attractor can be hidden, e.g. trivial (fixed points) and global attractors of dynamical systems generated by ODE in Euclidean space cannot be hidden according to the classification. Thus, the situation is seems to be similar to the discussion of limit cycles (periodic attractors): while this notion is mentioned in the article on attractors Attractor there is a separate rather long article on limit cycles where effective methods for the study of limit cycles and corresponding open problems are discussed. Thus, the idea of merging this article with the article on attractor does not seem obvious to me.

Given all this, I suggest to remove Template:Neologism. Also I suggest to remove Template:Third-party, taking into account that according to Reliable_sources: “Material such as an article, book, monograph, or research paper that has been vetted by the scholarly community is regarded as reliable, where the material has been published in reputable peer-reviewed sources or by well-regarded academic presses”. Remark, that notions in the mathematics are usually used with references to the pioneering works where the notions were introduced. Also I have found that a figure with coexisting hidden Chua attractors was chosen for the cover page of the International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, volume 27, number 12, 2017: https://www.worldscientific.com/na101/home/literatum/publisher/wspc/journals/content/ijbc/2017/ijbc.27.issue-12/ijbc.27.issue-12/20171218/ijbc.27.issue-12.cover.jpg KudryashovaLenaPhDMath (talk) 09:13, 16 March 2019 (UTC)


 * Taking into account the above and since there is no discussion, I remove these template messages.KudryashovaLenaPhDMath (talk) 22:32, 17 April 2019 (UTC)