Talk:Van der Pol oscillator

stability

I think this should explain why the system is stable for mu > 1.

Perhaps the transfer function poles could be analyzed... —Preceding unsigned comment added by 99.235.199.57 (talk) 01:42, 5 February 2008 (UTC)

Adding more detail...

I modified the article twice (one is anonymous since I forgot to log in) and removed the forcing function from the right-hand side of the equation. I'll eventually add in a sentence or two explaining the subtraction/addition of energy to the system based on the magnitude of x and the qualitative difference between the limit cycles when epsilon << 1 and when it is larger (relaxation oscillations). The forced van der Pol oscillator should be the subject of a subsection of this article. Rompala

Accidently pressed save when checking for the last time so no comments on history. However, added short section on the forced oscillator, a history with a few uses and references and a section showing what happens to the unforced oscillator for varying values of mu.Kae1is 17:17, 17 November 2006 (UTC)

Revisions & Suggestions

Removed second, point link to non-linearity, improved dynamics link - especially as it's now been moved to Category:Chaotic maps. Added hypens so gramatically correct. I'm sorry whoever changed it but the van is not capitalised, see Balthasar van der Pol and half the instances in this article and his own article in Nature. Finally found the correct reference for the seismology comment it's only taken me 5 years.

I can prove the other results I provided earlier (I can give you the program and the values required to obtain the results given); but it's not been published so I understand if nobody wants to use them. I don't like the word regimes in the results section... it just sounds wrong. If anyone has any better suggestions that'd be good.

I have numerous phasemaps and FFTs of the VDP and forced VDP oscillators, though unfortunately not in colour, that'd I'd be happy to add, they're all created by me using a program that I wrote, along with values of A, E μ and ω. Kae1is (talk) 21:30, 26 October 2009 (UTC)

Re capitalization of Dutch names, the info above is actually only partially correct. While it is true that the 'V' in "Balthasar van der Pol" is not capitalized, it should be capitalized when the last name appears without the first (as in "Mr. Van der Pol"). This is admittedly a strange convention (even stranger: in the Dutch phonebook you would find Mr. Van der Pol under the letter "V"), but it goes for all Dutch names that begin with articles ("Van", "Van der", "Van de", "De"). Therefore, while the man himself is called Balthasar van der Pol, the oscillator is actually the Van der Pol oscillator. Also see Dutch name for more info. Inkie23 (talk) 22:33, 6 November 2011 (UTC)

Merging from the Dutch version?

The Dutch version of this page contains much more information, would anyone be interested in a translation? It also uses a more consistent notation for the nonlinear term. 131.180.16.252 (talk) 13:02, 30 November 2009 (UTC)

Limit Cycle Plot

Hi there, I've added a plot to show how the limit cycle changes with μ in phase space. I hope this is helpful. Suggestions welcome. --widdma (talk) 11:11, 9 February 2010 (UTC)

that is great but....

what is it? for a article on an electrical circuit, it doesn't have a single diagram --UltraMagnus^speak 18:38, 12 May 2010 (UTC)

Scholarpedia has a picture of the circuit: http://www.scholarpedia.org/article/File:VdP-circuit.gif ; I don't know what their licensing terms, etc, are, if we can just copy/paste it here. Some dutiful wikipaedian want to do that for me? Charibdis (talk) 10:01, 17 November 2010 (UTC)

It doesn't have "a circuit", or at least not any one single canonical circuit. These oscillators are a theoretical model for the behaviour of any number of circuits that give the model's behaviour. It would be useful to give such a circuit, but we should make it clear that this isn't the only possible circuit that would still be "a Van der Pol oscillator".

As to Scholarpedia, then their licence is CC-by-nc-sa, so it's not acceptable for use on WM projects. Contact the image author though - they might be willing to upload a copy under CC-by-sa. Andy Dingley (talk) 12:15, 10 March 2013 (UTC)

canards

Can someone add some information on canards here? Tkuvho (talk) 17:11, 10 May 2011 (UTC)

Needs much work

The article contains a great deal of important information.

Unfortunately, many, many portions of the article are written so briefly — or only for readers who are already experts in this subject — that most readers will find it extremely difficult to comprehend.

I hope someone who is knowledgeable about this subject will add enough detail so that the article becomes comprehensible — at least to readers with a basic background in differential equations.

Currently, it is not.

Example

Easy to see at https://polyphys.com/centralflow.php when the "Q" handle (controlling flow character) is more than 90deg from vertical in either direction. You can even make one stable limit cycle inside another with the right configuration. I always wondered what this effect was called but just learned the phrase "limit cycle" today. 162.246.139.210 (talk) 21:24, 19 January 2024 (UTC)