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Chaos a new science6/25/2023 ![]() ![]() ![]() We often say observations are chaotic when there is no discernible regularity or Through measurement, and that these observations or measurements vary unpredictably. "The very use of the word 'chaos' implies some observation of a system, perhaps ![]() Space appears to be quite random." Finally, Rasband (1990, p. 1) says, ![]() Whose outcome is very sensitive to initial conditions (i.e., small changes in initialĬonditions lead to great differences in outcome) and whose evolution through phase Says, "By a chaotic solution to a deterministic equation we mean a solution Of more than one orbit) will be called chaotic." Tabor (1989, p. 34) Sensitive dependence on initial conditions on a closed invariant set (which consists For example, Wiggins (1990, p. 437) says, "A dynamical system displaying It turns out that even textbooks devoted to chaos do not really define the term. For example, he quotes Philip Holmes (apparently defining "chaotic") as, "The complicated aperiodic attracting orbits of certain, usually low-dimensional dynamical systems." Similarly, he quotes Bai-Lin Hao describing chaos (roughly) as "a kind of order without periodicity." Gleick (1988, p. 306) notes that "No one could quite agree on the word itself," and so instead gives descriptions from a number of practitioners in the field. In fact, it is much easier to list properties that a system described as "chaotic" has rather than to give a precise definition of chaos. ![]()
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