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Chaos Unmasked

In a ground-breaking project, researchers from Massey University's Department of Physics have developed a dynamic system that allows them to put a face to chaos.

Physicists Chris Reid and Scott Whineray have constructed a mechanical oscillator, the chaotic motion of which is tracked ultrasonically and observed on a computer in real time. The development is significant, not just because it is experimental rather than computer simulated, but because it is versatile -- it permits the study of a variety of potentially chaotic systems, rather than just one and, in addition, the oscillation is uncommonly large.

Chaos refers to the behaviour of a system whose final state depends so sensitively on the initial state that the behaviour is eventually unpredictable despite extremely accurate knowledge of both the governing equations and the starting conditions. One example is the weather, the predictability of which is about three days; another example is the currency market.

But chaos is not random -- there is an "order", the signature of which is referred to as a "strange attractor". The system's underlying equations determine the strange attractor's pictorial character.

The new apparatus consists of a glider floating on an air track and compelled by a regular impulse to oscillate between two potential troughs established by a unique spring configuration. Every time the impulse fires, the position and speed of the glider are measured and instantly displayed as a point on the computer screen. Dr Peter Kay of the Computer Science Department has assisted with the software for the computer interface.

The resulting image is called a Poincaré plot, after Jules Henri Poincaré (1854-1912), a French mathematical physicist who developed the idea well before chaos was recognised around 1960. With normal regular oscillation the plot has a "simple attractor" of one point, or perhaps a few points. With chaotic motion the result is an unlimited number of points -- the strange attractor.

"The versatility of this new system enables a number of complex and mathematically elusive non-linear oscillations to be examined," Whineray says. "It is a wonderful pedagogical tool as well."

The applications of chaos research are wide. For example, the two-trough case can be used to model ion plasma vibrations, while another pattern under investigation mimics the variable beat of an arrhythmic heart.

"Once you understand how chaotic patterns occur, you can also investigate how to shut them down. For example, with an arrhythmic heartbeat, as with unstable laser oscillations, it is possible to stop the chaotic behaviour by imposing a small stabilising impulse, thereby regaining a regular heartbeat," Whineray says.