The Undead and the Hopf Bifurcation Theorem


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The Undead and the Hopf Bifurcation Theorem

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Edited: Oct 9, 2013, 6:06pm

Since Halloween is later this month...

Cycles of fear: Periodic bloodsucking rates for vampires.

Journal of Optimization Theory and Applications, December 1992.


In this paper, we present a new approach for modelling the dynamic intertemporal confrontation between vampires and humans. It is assumed that the change of the vampiristic consumption rate induces costs and that the vampire community also derives some utility from possessing humans and not only from consuming them. Using the Hopf bifurcation theorem, it can be shown that cyclical bloodsucking strategies are optimal. These results are in accordance with empirical evidence.

For more on optimization in the presence of undead agents, see the Economics group here.

Edited: Oct 9, 2013, 6:10pm

Here's a page in which they mention the foregoing paper, noting that vampire-human dynamics can be analyzed in the context of a Lotka-Volterra predator-prey model.

Also, the photo is... yummy.

Edited: Jul 6, 2017, 3:36pm

Speaking of scary stuff involving math, try this story, by Math teacher Ben Orlin. It's at his Math With Bad Drawings blog.

The Differentiation: A Survivor’s Tale.

Seriously got goosebumps at the end.

ETA: Clarification.

Edited: Jul 6, 2017, 3:43pm

My humble attempt at a sequel blog post:

The Killer and the Healer

Note: Not as good as the original; don't expect too much!

- - - - - - - - - -
Edit after flagging: Just a blog post at my blog, not a book, I swear!

Hmmm, link is now dead anyway, I guess because of the flags. Gah.

Jul 6, 2017, 12:26pm

Yikes. That will teach me to not check into LT for several days.

I have to be away from the computer for a while, but will be back later. Meanwhile, anyone who flagged the post and wants to chime in with the specific violation(s) - I will fix by altering or deleting it. (If you don’t want to out yourself, no pressure.) Also, Lyndatrue, I saw that you provided links, thank you, will carefully read them soon. Hopefully that will clarify.

Edited: Jul 6, 2017, 12:57pm

>5 TFleet: Specifically:
The ToS links to Tips and Guidelines for Authors, where it says
Do not post messages in Talk advertising your book. You can promote your book in Hobnob with Authors, but posting a blurb about your book and never coming back to discuss it is still seen as overt advertising.

A lot of people here take this very seriously, and on the principle of the Camel's nose, don't take any chances.

ETA: I was not one of the people who flagged your post.

Edited: Dec 28, 2017, 2:58pm

>6 Foretopman: Thank you for clarifying!

The thing I linked to in #4 was just a blog post at Ben Orlin's Math With Bad Drawings blog, and the "sequel" I mentioned in #5 was just a blog post that I wrote following on (with the original author's permission). It's not a book, just a humorous mathy blog post, I swear!

My wording was obviously bad, so am going to edit both posts.

Edited: Jul 6, 2017, 3:56pm

I think the fact that you are an author and most of your profile is devoted to promoting your book (which is 100% allowed), plus the use of the word "sequel", made people think this was self-promotion.

(I didn't look at either link. I don't do scary. But now you say it's humor?)

Jul 7, 2017, 9:12pm

>8 lorax: Thanks for feedback!

I think the fact that you are an author and most of your profile is devoted to promoting your book (which is 100% allowed)...

Yeah, I was pretty sure it’s allowed, but it’s nice to have confirmation. But I am going to check out some “LT Authors” profiles to get a sense of site norms. (Someone once said, “I’d rather have control over a country’s customs than its laws.”) the use of the word "sequel" Yeah, I think that word was a big part of the problem.

I don't do scary. But now you say it's humor?

It’s not at all scary, really. In Orlin’s original post, SPOILER WARNING mathematical functions are being attacked by a merciless operator called... the Differentiation. In the first wave of attacks, quadratics become linears. Then linears become constants, and then...

Seems cutesy, but in the comments, a mathematician said it gave him chills. Me too. So I wrote a “sequel” post about a mysterious healer who can resurrect differentiated functions... Mine was more of a noir/police procedural, heh.