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