Deterministic Chaos (1927? - )

 


 

Deterministic chaos, often just called "chaos", refers in the world of dynamics to the generation of random, unpredictable behavior from a simple, but nonlinear rule. The rule has no "noise", randomness, or probabilities built in. Instead, through the rule's repeated application the long-term behavior becomes quite complicated. In this sense, the unpredictability "emerges" over time.

There are a number of characteristics one observes in a deterministically chaotic system:

Professor James Yorke, an applied mathematician at the University of Maryland, is often credited with associating the word "chaos" with these particular mechanisms, in the late 1970s. While it has helped the field of nonlinear dynamics to have a simple, handy word like "chaos", the word itself is a bit of a misnomer. In fact, the word is downright confusing, if one interprets it in the nontechnical sense of common language--"lack of order". In fact, deterministic chaotic systems are quite ordered and even predictable on short time scales. In many ways modern dynamicists study deterministic chaotic systems to understand the interplay between order and "utter chaos". The goal is to find the hidden order in the apparent chaos.

One of the earlist known experimental reports of deterministic chaos occurred during 1927 in the Britsh scientific journal Science. A brief letter to the editor, only two pages long, by the Dutch electrical engineer Balthasar van der Pol and his colleague van der Mark, reports on the "irregular noise" heard in a telephone earpiece attached to an electronic tube circuit. Unfortunately for the authors, the paper discounts this phenomenon and instead the paper concentrates on various periodic, predictable behaviors that sounded like "bag-pipes" and were found in other non-chaotic regimes of the circuit.

Today deterministic chaotic behavior has been discovered in numerous natural phenomena and analyzed in detail in dozens of experiments. From compound pendula to dripping faucets, from predator-prey ecologies to measle epidemics, from oscillating chemical reactions to irregular beats of a chicken heart, the underlying mechanisms have been detected. Despite the scientific successes, though, it is important to emphasize that deterministic chaos, and the various mechanisms that underlie it, are not the only explanations of random, noisy, unpredictable behavior in nature. Many well-known processes, and undoubtedly many waiting to be discovered, can produce behavior that is unpredictable. Thus, this abiding question is, How do we discover which of many possible mechanisms has produced the apparent disorder?

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