Chaos Theory: Is It Still Being Studied?

[Jake4]

So I've recently been reading up a bit on Chaos theory. It seems like a pretty cool idea (that's all I can say about it, because I don't have a true, full understanding of it) but my question is this:

Is it still being studied?

I'm reading CHAOS by James Gleick(basically the definition of lay person's pop-sci book) in which they make it sound like the best new thing since sliced bread. However, it was published in 1987, and I just wanted to know if it is still as hotly pursued as it once was?

 

[HallsofIvy]

It is now a recognized sub-field of mathematics but "sliced bread" it isn't. I think its "shining moment" came in "Jurassic Park", where Jeff Goldblum played a mathematician who kept chattering about "Chaos Theory"- what he said mostly proving that he had no idea what it was about!

 

[Studiot]

From Calculus to Chaos by David Acheson

Would be a good book to follow Gleik if you seriously wanted more.

 

[jackmell]

Also "Chaos and Fractals" by Peitgen is the classic (popular) reference. Guess I think it is slice bread. Why do I think that? Gotta' good reason but lii' hard to explain. A lot of phenomena in nature are non-linear and subject to chaotic behavior. Like what Jack, I say to myself? Weather, . . . lemme' just Wikipedia it:

"Chaotic behavior has been observed in the laboratory in a variety of systems including electrical circuits, lasers, oscillating chemical reactions, fluid dynamics, and mechanical and magneto-mechanical devices, as well as computer models of chaotic processes. Observations of chaotic behavior in nature include changes in weather,[4] the dynamics of satellites in the solar system, the time evolution of the magnetic field of celestial bodies, population growth in ecology, the dynamics of the action potentials in neurons, and molecular vibrations. There is some controversy over the existence of chaotic dynamics in plate tectonics and in economics.[12][13][14]

One of the most successful applications of chaos theory has been in ecology, where dynamical systems such as the Ricker model have been used to show how population growth under density dependence can lead to chaotic dynamics.

Chaos theory is also currently being applied to medical studies of epilepsy, specifically to the prediction of seemingly random seizures by observing initial conditions.[15]

A related field of physics called quantum chaos theory investigates the relationship between chaos and quantum mechanics. The correspondence principle states that classical mechanics is a special case of quantum mechanics, the classical limit. If quantum mechanics does not demonstrate an exponential sensitivity to initial conditions, it is unclear how exponential sensitivity to initial conditions can arise in practice in classical chaos.[16] Recently, another field, called relativistic chaos,[17] has emerged to describe systems that follow the laws of general relativity."

I've done quite a bit of (non-professional) work in Chaos Theory so I am partial to it. Also, "Chaotic Dynamical Systems" by Devaney and while you're at it, his book "Differential Equations", by Blanchard, Devaney and Hall.

Also T. Sejnowski (author of "The Computational Brain") suggests strange attractors, a particular form of chaos, may exists in the brain and serve some memory function, and I have personally observed Feigenbaum behavior in back-propagated neural networks.

Describing (strange) attractors of chaotic dynamical systems is an achievements of Chaos Theory. While I'm on a roll, I should not exclude Rene' Thom and his work with a closely-related field Catastrophe Theory where he uses the concept of strange attractors to describe the process of morphogenesis in living systems.

 

[SW VandeCarr]

Here's an interesting description of a chaos theoretical model of cell cycle oscillations as it relates to cancer pathogenesis.

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1891444/