Thursday, October 31, 2013

Using Chaos Theory to Predict "Dragon King" Events

From Wired Magazine:

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.”
... in the last few years, scientists in many fields have been looking closely at the behavior of extreme events – very large fluctuations in a system that often leads to catastrophic results. These occur in many complex, chaotic systems: enormous rogue waves in the ocean, extreme weather in the climate, or global stock market crashes.

One particular class of these extreme events is known as a dragon king event. This is a catastrophic occurrence that falls far outside a normal expected probability. The name comes from looking at the wealth distribution in a medieval society. If you plot the number of people who have a particular amount of wealth, you would see many, many poor farmers and a smaller number of wealthier landowners and noblemen. Plotting the number of people versus a given amount of wealth would give you a straight line.

Now the medieval king, who typically has an enormous amount of wealth, would be outside this plot, far above the rest. Think of someone like Bill Gates or Carlos Slim whose wealth dwarfs even that of a modern one-percenter. While the rest of the population is described by the simple line plot, these people are outliers.

So why dragon kings? Because, like dragons, certain extreme events are entirely outside the normal classification scheme. “Dragons are extraordinary animals of extraordinary properties,” said economist Didier Sornette of the Swiss Federal Institute of Technology Zurich, another co-author of the work.

Dragon king events may be freakish, but they are not freakishly rare. In fact they occur much more frequently than you would expect. ...
 The article describes the history of the research into these events. It also notes that detecting an upcoming event doesn't mean that it can be stopped because it may be impossible to affect any changes to the system--the article uses the example where ocean temperature is a variable is not one we could change.

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