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Delayed feedback

I made a new article about delayed feedback, since I introduced the concept in the logistic equation article. It's related to stochastic delay differential equation but as always I think it's good to separate the qualitative features that don't come from stochasticity. In this case, the fact that if you add delay to your favourite ODE you probably break its (in)stability properties in some regimes. Which then means that the equation amplifies noise and therefore both numerical approximations and stochastically driven versions are likely to be problematic.

The article is still half-cooked.

Comments

  • 1.

    I have now expanded the article with a short analytical discussion of instability of a particular delayed-feedback system:

    $$ \dot x(t) = - x(t-\Delta) $$ and some observations about the implications for numerical stability and the noise-driven version.

    Comments solicited.

    To reassure myself about the claims I have been doing some numerical experiments with R which I should probably add to the wiki in the vein of Staffan Liljegren's Experiments in predator-prey in Sage.

    Comment Source:I have now expanded the article with a short analytical discussion of instability of a particular delayed-feedback system: $$ \dot x(t) = - x(t-\Delta) $$ and some observations about the implications for numerical stability and the noise-driven version. Comments solicited. To reassure myself about the claims I have been doing some numerical experiments with R which I should probably add to the wiki in the vein of Staffan Liljegren's [Experiments in predator-prey in Sage](http://www.azimuthproject.org/azimuth/show/Experiments+in+predator-prey+in+Sage).
  • 2.
    edited February 2011

    GREAT!

    I really want to write about the delayed action oscillator and El Niño in This Week's Finds. When I do it, I'll take advantage of all the stuff we have on the Azimuth Wiki, credit everyone who helped, and link to it.

    Yes, please add your R code to Delayed feedback, just as Graham did in Quantitative ecology.

    By the way: we follow the Wikipedia conventions on capitalizing page titles. So, I changed the title of your page from delayed feedback to Delayed feedback. This process creates a redirect so that now both links work.

    I also added

    category: mathematical methods

    to the bottom of your page. This makes it easier for the lab elves to add a link, and someday a description, to the page Methodology.

    I'm so happy you've joined our team!

    Comment Source:GREAT! <img src = "http://math.ucr.edu/home/baez/emoticons/thumbsup.gif" alt = ""/> I really want to write about the delayed action oscillator and El Ni&ntilde;o in This Week's Finds. When I do it, I'll take advantage of all the stuff we have on the Azimuth Wiki, credit everyone who helped, and link to it. Yes, please add your R code to [[Delayed feedback]], just as Graham did in [[Quantitative ecology]]. By the way: we follow the Wikipedia conventions on capitalizing page titles. So, I changed the title of your page from [[delayed feedback]] to [[Delayed feedback]]. This process creates a redirect so that now both links work. I also added `category: mathematical methods` to the bottom of your page. This makes it easier for the lab elves to add a link, and someday a description, to the page [[Methodology]]. I'm so happy you've joined our team!
  • 3.

    Now done...

    Comment Source:Now done...
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