Saturday, November 2, 2013

"Using Chaos Theory to Predict and Prevent Catastrophic ‘Dragon King’ Events"

From Wired:
A strange attractor plotting the behavior of a chaotic system. New research suggests that some chaotic systems could contain particular variables that can predict and stop extreme events from occurring. Image: Nicolas Desprez/Wikimedia
Stop a stock trade and avoid a catastrophic global financial crash. Seal a microscopic crack and prevent a rocket explosion. Push a button to avert a citywide blackout.

Though such situations are mostly fantasies, a new analysis suggests that certain types of extreme events occurring in complex systems – known as dragon king events – can be predicted and prevented.

“A chaotic system may be in flux, and look like random behavior,” said physicist Daniel Gauthier of Duke University, co-author of a paper appearing Oct. 30 in Physical Review Letters. “But maybe there’s some internal structure we can identify that leads to destabilizing events.”

By looking at a simple experimental chaotic system, Gauthier and his co-authors have been able to detect telltale signs that a dragon king event was approaching and, most importantly, stop it from happening. If this work can be generalized to more complex systems, such as climate, power grids, and financial markets, it could be used to forecast and perhaps forestall extreme behavior.

The story of this finding begins in the mid-90s when Gauthier was studying the behavior of simple electronic circuits that were trained to follow one another. His team did this by periodically measuring the difference in either the voltage or current between the two circuits. They would use this difference to give one system a tiny kick. The idea was to synchronize the circuits as much as possible. And, for the most part, it worked: One circuit followed the behavior of the other.

But occasionally, the two circuits would get out of whack. Essentially, the leader circuit was losing control of its follower, which would go off on its own and exhibit completely different behavior. This desynchronization event would eventually get corrected – the tiny kicks would push the follower circuit back to the same behavior as its leader. But the results remained a bit of a head scratcher, until Gauthier figured out what was going on.

Chaotic systems are often very simple. They can be characterized by just  a few parameters – in this case the voltage and current of the circuit – but they also exhibit random and unpredictable behavior. Yet the voltage and current of the system can’t take on just any value. Instead, the parameters will stay within a somewhat narrow range. The possible values within this range are what mathematicians call a “strange attractor.” When plotted on an x and y axis, strange attractors often take on odd shapes, sometimes looking like the wings of an arithmetic butterfly.

The meeting points of these two wings – the “body” of the butterfly – was where the desynchronization was happening in Gauthier’s circuits. Imagine one circuit is traveling around on a wing of the butterfly, pulling the follower circuit slightly behind it. From time to time, the leader circuit would enter the meeting point of the wings and jump to the opposite side. Usually, the follower circuit would come right along with it but, every so often, the difference between them would be just enough so that the follower circuit wouldn’t make the hop, instead staying on the same wing....MORE
HT: The Big Picture