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Chaos Theory

The Chaos Theory

The word "chaos" is sometimes taken to mean the opposite of "cosmos", in that the latter term has connotations of "order". Until the last few decades, chaotic systems have not been studied nearly as much as ordered systems, perhaps because chaotic systems are far more difficult to understand...

What is a chaotic system?

Looking at the rising smoke from a cigarette illustrates some of the differences between ordered and chaotic systems. Initially the smoke rises in a smooth upward flow (laminar flow), which breaks down a few inches above the tip of the cigarette into a disordered, turbulent motion(turbulent flow). This is an example of a transition from an ordered system into a chaotic one. A stream of water flowing out of an appropriately adjusted faucet exhibits similar behaviour, which is ubiquitous in a host of phenonomena, both man-made and natural. The weather systems of the atmosphere (which are intertwined with the heat and mass flows in the oceans) are chaotic. A system of more than two bodies orbiting under each other under their mutual gravitational attraction is also chaotic, by extension the entire solar system is a chaotic!

One non-technical definition of a chaotic system goes as follows: A chaotic system is one in which a tiny change can have a huge effect. Thus the oft heard statement that a butterfly in China can cause a hurricane in the Atlantic. What makes the situation even more difficult is that we have only recently begun to forge the mathematical tools necessary to study these problems. As usual, some of the seminal works on chaos were performed by physicists of the former USSR, whose work received scant attention until recently; although today, chaotic systems are being extensively studied both experimentally and theoretically.

Acoustics of the Chaos Theory