Can anyone give me some examples of practical applications of chaos theory in engineering or physics?

Do you know any good books about chaos theory or its applications?

  • 1
    $\begingroup$ This reminds me, someone came up with a list of the 20 or so most important equations, which I saw posted on Facebook, and one of them involved chaos, and I doubted it belonged on the list because there were probably at least 20 more important equations. Has everyone seen that list? $\endgroup$ Nov 11, 2013 at 20:53
  • $\begingroup$ It is from the book In Pursuit of the Unknown: 17 Equations That Changed the World by mathematician Ian Stewart (see e.g. [1, 2]). The logistic map representing the chaos theory is number 16. in the list. $\endgroup$
    – EditPiAf
    Oct 19, 2017 at 13:11

3 Answers 3

  1. Using chaotic circuits for digital communications: For example, here, here, and here. There are hundreds of papers like this. My thesis advisor took a year off to do research for NASA on this very subject several years back.

  2. Modeling chaos in neuronal action potentials, modeling neuronal action potentials with nonlinear systems that have chaotic windows, and mathematical analysis of such models: For example, here, here, here, and there are hundreds more like this. I did my master's thesis on modeling cardiac action potentials with Van Der Pol equations. Balthasar Van Der Pol himself made this model to approximate the behavior of a triode circuit, and his "fuzz" back then corresponds to my "chaotic window" today. He was a radio engineer and research physicist, so there is a tight connection for you.

  3. Edward Lorentz actually made the Lorentz equations as a dramatically simplified model of convection rolls in the atmosphere, but you would probably call that Meteorology. However the chaotic waterwheel (in video) would be a physics application. Here an undergrad did a nice paper on the subject for his physics degree. The system that models the chaotic waterwheel is an analog of the Lorentz equations. I first found this reading Strogatz, although many have written on this subject. This is actually an amazing demonstrable relationship.

  4. This guy is a friend of my advisor. He is an expert at forming electronic circuit analogs of mathematical models for industry (a get paid big bucks to take theory and test it in physical reality sort of thing), and a prolific well cited author. Look at some of those papers. you will see the word "Chaos" regularly, and his papers are brilliant. You should be able to read many of those papers indirectly from that google cite link. He does alot of work with Josephson Junctions as you will see in his papers.

If you like electronics engineering and "chaos", you might be able to make a good living just writing papers with the words "chaos" and "Josephson" in the same sentence, like here is an example but there are hundreds. (note I am being non-serious/silly here, there are just so many papers!)

Book Recommendation: If you have no books, get Nonlinear Dynamics and Chaos by Steven Strogatz. That would be my number one first book pick, and it does have plenty of applications in "physics and engineering" for you to work on. After you get that first book and read it, reread it and attempt all of the problems. After doing this, you will have enough information to broach the question of "next book" rest assured.

  • $\begingroup$ Your link to chaotic waterwheel is dead now. $\endgroup$
    – Ruslan
    Jan 31, 2018 at 14:42

Here are the two that I am very familiar with:

1). http://www.whydomath.org/node/space/index.html

Use of chaotic properties of the three-body and n-body problems to design low fuel space missions

To learn more, google scholar "restricted three body problem, space missions"

2). http://gmwgroup.harvard.edu/pubs/pdf/773.pdf

Designing micro mixing devices which use chaos to efficiently mix fluids, at a rate which is not possible without chaos.

To learn more, google "chaotic mixing"


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