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Surprising relationship between chaos, order

April 26, 2006
Courtesy Washington University in St. Louis
and World Science staff

One of nature’s most baffling, perhaps deepest puzzles may seem quite removed from the grand questions scientists love to ponder—the fate of the universe, the nature of the invisible “dark energy” filling it, and the like.

A violin can be envisioned as a system of "coupled" oscillators, vibrating things (strings) that are connected together so that each oscillator influences the motions of neighboring ones. (Photo courtesy stock.xchng)

The mystery has to do with a class of common events that can occur in full view, and share one key feature. In them, chaos inexplicably leads to greater regularity, or synchrony.

In certain experiments, “When you introduce disorder… the chaos that was present before disappears and there is order,” said Sebastian F. Brandt, a physics graduate student at Washington University in St. Louis.

Brandt and colleagues conducted a study that explored the conundrum, and which appeared in the January issue of the physics journal Physical Review Letters. The researchers said they found a surprising mechanism at work.

The researchers worked on a computer simulation of a network of pendulums. They chose pendulums as representative of a wider class of objects known as oscillators. 

An oscillator is anything that somehow swings back and forth rhythmically when disturbed. Under the right conditions almost any sorts of objects, including atoms, can be oscillators. 

The “pendulums” in the simulation were loosely connected to each other, as oscillators also are in many natural situations. A textbook example of such “coupled” oscillators is pendulums with springs linking their ends together. Other common cases are violin strings, which are connected by their sounding boards, and electrical filters used in communications. 

The scientists found that the pendulums, when pushed by forces according to a regular rhythm, behaved chaotically and swung out of sync. Yet when the researchers introduced disorder—applying forces at random intervals to each oscillator—they began to swing in synch. The “forces” were applied along the rods of the “pendulums” to make them swing. 

Physicists are as bewildered by all this as anyone else, said Ralf Wessel, a Washington University physicist who supervised the study: “Every physicist who hears this is surprised.”

Scientists have long been intrigued by the relationship between order and disorder, sometimes pointing to the emergence of life as an example of how order itself can arise from chaos. 

Sometimes chaos can seemingly create its opposite. An example that might come to mind is that old favorite way of fixing a broken TV set—hitting it. Occasionally this solves the problem, but not always, Brandt said, showing that the principle only goes so far. 

It in fact works only with certain systems, Brandt added. The much more common situation is the other way around, where “disordered processes destroy spatial and temporal regularity,” he wrote in an email.

Research on the role of disorder in “complex” systems such as coupled oscillators is quite new and poorly understood, the researchers said. But they argued that their model could shed light on real-life processes. 

Brain cells, for example, have been studied as coupled oscillators because of the way they interact. They sometimes appear to display repetitive electrical activity affected by neighboring cells’ activity.

Though it’s a bit of a stretch, the study may help to solve previously unexplained findings, said Babette Dellen, a member of Brandt’s team. Brain cells, she explained, can act in synch in response to a stimulus, but no one knows why. “Maybe the details of neurons [cells] are completely irrelevant,” Wessel remarked. “Maybe it is only a property of oscillators.”

A key similarity between the simulated system and neurons is that they are both “nonlinear,” the researchers said. This means the applied force has no straightforward relationship to the distance moved.

A linear system is like a child being pushed gently on a swing. He’ll move in proportion to how hard you push: push twice as hard, and he’ll go twice as far. But past a certain height, pushing twice as hard won’t double the distance. The system is now nonlinear.

Nearly all complex systems in nature are nonlinear, like the physicists’ model, they explained. So are neurons, which is why “when you hear your favorite music twice as loud you don’t double the pleasure,” Brandt said. 

Previous research had also shown that disorder can create order. But past studies often involved manipulating properties of the system itself, such as changing pendulum length, Brandt added.

What’s new in this study, he said, is that it involves changing externally applied forces. Thus, he argued, the findings might be applicable to the real world, where it would be hard to change things within the system—neurons, for example—but easier to apply external forces. “It will be interesting to see if the mechanism that we have found can actually be put to some use,” Brandt said.

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