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Achieving control of chaos at high speeds.

Steering a car around a corner generally requires more than a steady hand. Most drivers must periodically adjust their estimates of how far to turn the steering wheel before they safely emerge from a curve. Few manage to keep the steering wheel's orientation fixed throughout the entire maneuver.

Nudging a chaotic system so that its erratic behavior settles into a regularly repeating pattern requires a similar approach (SN: 1/26/91, p.60). Troy Shinbrot, a physics graduate student at the University of Maryland in College Park, and his collaborators have now demonstrated just such a technique for rapidly directing a chaotic system to a particular type of periodic motion. Taking advantage of a chaotic system's extreme sensitivity to initial conditions, they use a series of tiny, judiciously chosen and carefully applied perturbations to maneuver its behavior into the type of periodic motion desired.

Shinbrot and his colleagues worked with a metal strip -- resembling stiff tinsel -- made from a specially prepared iron alloy that changes its stiffness in accordance with the strength of an applied magnetic field. Periodically changing that field causes an upright ribbon to alternately bend and straighten as the ribbon softens and stiffens.

For certain strengths and frequencies of the applied magnetic field, the strip arbitrarily and abruptly shifts from one position to another. Researchers can "map" these chaotic motions on a diagram showing how the strip's position changes with each cycle of the alternating magnetic field (see illustration). Such a map, or "attractor," shows an array of scattered points. An equivalent diagram representing a motion that precisely repeats itself every cycle would display a single point.

By periodically adjusting the magnetic field in just the right way, researchers can keep the ribbon from moving chaotically. It settles into a repeating motion that coresponds to a particular point on the attractor. But to get it to that point, where control of the chaotic motion becomes possible, researchers normally have to wait until the chaotic system's motion, as depicted by its attractor, happens to land near the desired point.

Shinbrot and his colleagues show that a succession of small, carefully selected changes in the magnetic field can bring a chaotically oscillating ribbon from some initial position to the desired behavior in far less time than required by waiting for the system itself to come around to this type of motion.

These experimental results, presented by Shinbrot at last week's Experimental Chaos Conference in Arlington, Va., demonstrate that earlier theoretical work by the Maryland group has validity for real physical systems. For instance, computer simulations showed that one particular chaotic system, left on its own, would require, 6,000 steps to reach its target, whereas the use of small perturbations would cut the number of steps to 12.

"Our work can be interpreted as a means of controlling or limiting the troubles that chaos causes," Shinbrot says. "I prefer the view that our work opens up new possibilities for designing chaos into systems." This might provide new insights into how biological organisms switch so easily from one state to another, he adds.
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Title Annotation:making chaotic systems regular
Author:Peterson, Ivars
Publication:Science News
Date:Oct 12, 1991
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