Some of the more recent dramatic disasters in world-wide markets have occurred, not because people panicked or an election did not go someone's way, but because financial institutions have taken to hiring physicists who wrote papers on predicting chaos.

If non-linear is just linear in really small steps, then predicting and controlling nonlinearity is manageable. But those extreme chaotic events, the "dragon kings", have not obeyed numerical models yet.

An upcoming paper in Physical Review Letters seeks to tame that savage chaotic breast again, with a simple model of chaos predicting that it is possible not only to predict an extreme event, like a stock market collapse, but to intervene and prevent it from happening.

Didier Sornette of the Swiss Federal Institute of Technology, director of the Financial Crisis Observatory, coined the term "dragon king.




Dragon kings are less random than thought, the researchers say and in true nonlinear-is-just-linear-in-small-steps, find they can be anticipated and controlled.

The latest finding is an outgrowth of experimental work 
co-author Dan Gauthier, the Robert C. Richardson professor of physics at Duke University
has been doing since the 1990s with simple electrical circuits he calls "chaos generators." Two identical circuits consisting of two capacitors, an inductor, a nonlinear diode and a power source, are each set to generate chaotic oscillations in their voltages and currents.

Being identical, the credit-card sized circuit boards are supposed to oscillate in synch with each other when they are coupled - called "synchronized chaos." But in practice, they experience subtle variations in behavior so that the voltages and currents in one circuit do not match their twin.

Because the behavior of each circuit is chaotic, the voltages and current change in an erratic manner over time, but both circuits are synchronized, so that they both change together and show the same behavior most of the time, Gauthier said.

During a long run of the experiment, the data reveal that the chaotic behavior visits "hot spots" in which an extreme event, "a bubble," might occur. This is an event in which the circuits suddenly and temporarily loose synchronicity. Sometimes the size of the event is small, like a small change in a financial market, and other times it is gigantic, like a market crash. And the size of most of these disturbances follows a power law distribution, in which one variable changes as a power of the other. The most extreme events, the "dragon kings," are responsible for significant deviations from the curve of the power law.  

Extreme events that may be governed by these laws would include sudden population crashes in species or freak waves in the ocean, Gauthier said. Other examples might be epileptic storms of activity in the brain and rolling power outages caused by an initial small disturbance, like a squirrel shorting out one substation on a large grid. Other examples could be found in the occurrence of incipient failure of materials and of engineering structures, in the synchronized behavior of kidney and heart cells in the body, in meteorological front dynamics and in climate change, among many others.

In a series of experiments performed with the coupled chaos circuits by co-author Hugo Cavalcante of the Federal University of Paraiba in Brazil, it was found that the introduction of a tiny amount of current injected into one of the circuits at just the right time prevented a predicted dragon king from happening. "Maybe tiny nudges can make a big difference," Gauthier said. 

"The limitation of our paper is that we haven't shown that our circuit has relevance to the stock market," which has many more variables, Gauthier said. "We aren't yet sure where to look, but for this one simple system, we figured out how to find it."