Personal AnecdoteI remember when chaos entered my life in the '60s (a chaotic decade). I reported to my manager that, as far as I could tell, the circuit behavior of my 20kHz "bang-bang" regulator was controlled by the phases of the moon. He did not take kindly to blaming the moon for my circuit's misbehavior. I changed to a PWM control and the problem went away. Later, when working with a discontinuous mode boost converter similar to that reported by Tse, I saw similar waveforms. In hindsight I feel vindicated in being perplexed. It was 20 years later, in 1984, when the problem was first discussed at a power electronics conference. We now know a lot more about it and more is becoming available.
On the WebChaos has been defined as - "Ancient God of the shapeless void that preceded the creation of the Earth,"
- "Extreme confusion or disorder," and
- "Stochastic behavior occurring in a deterministic system."
It has been used to explain many things, such as why we can't make long range predictions of the weather or the economy. If you are interested in learning more about chaos, a good starting point is The Chaos Hypertext book. More mundane is a FAQ sheet on chaos related terms. A sonnet by Edna St. Vincent Millay (1892-1950), I will put Chaos into fourteen lines, Sonnet X, gives it a poetic meaning. Millay died before the resurgence of mathematical chaos and could have known nothing of it, but the poem could describe the beauty of strange attractors as traced by computer graphics. You can see the beauty of some of these strange attractors in the Chaos Gallery at the Chaos at Maryland site, which is a good jumping off place for other links. A search on Chaos on Yahoo yields many other websites. But of recent interest are the new academic tagging websites where researchers can share their reference citations. For example, try CiteULike and search for chaos in title, author last name, abstract, journal name, or tag search types. You will get recent citations on the subject from a wide variety of scientific disciplines. The mathematically inclined may want to review the topic of chaos in Eric Weinstein's World of Mathematics on the Wolfram Research website. ReferencesTimeline of key papers: Historical development of problem and solutions Bibliography: Abstracts of source material. Complex Behavior of Switching Power Converters: Chi Kong Tse, The definitive book on chaos in power electronics Editor: Jerrold Foutz |
