chaos theory

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chaos theory,

in mathematics, physics, and other fields, a set of ideas that attempts to reveal structure in aperiodic, unpredictable dynamic systems such as cloud formation or the fluctuation of biological populations. Although chaotic systems obey certain rules that can be described by mathematical equations, chaos theory shows the difficulty of predicting their long-range behavior. In the last half of the 20th cent., theorists in various scientific disciplines began to believe that the type of linear analysis used in classical applied mathematics presumes an orderly periodicity that rarely occurs in nature; in the quest to discover regularities, disorder had been ignored. Thus, chaos theorists have set about constructing deterministic, nonlinear dynamic models that elucidate irregular, unpredictable behavior (see nonlinear dynamicsnonlinear dynamics,
study of systems governed by equations in which a small change in one variable can induce a large systematic change; the discipline is more popularly known as chaos (see chaos theory).
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). Some of the early investigators of chaos were the American physicist Mitchell Feigenbaum; the Polish-born mathematician and inventor of fractals (see fractal geometryfractal geometry,
branch of mathematics concerned with irregular patterns made of parts that are in some way similar to the whole, e.g., twigs and tree branches, a property called self-similarity or self-symmetry.
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) Benoit MandelbrotMandelbrot, Benoît B.
, 1924–2010, French-American mathematician, b. Warsaw, Poland, Ph.D. Univ. of Paris, 1952. Largely self-taught and considered a maverick in the field of mathematics, he was uncomfortable with the rigorously pure logical analysis prescribed by
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; the American mathematician James Yorke, who popularized the term "chaos"; and the American meteorologist Edward LorenzLorenz, Edward Norton,
1917–2008, American meteorologist and pioneer of chaos theory, b. West Hartford, Conn., Ph.D. Massachusetts Institute of Technology, 1948. Lorenz became interested in meteorology while working as a weather forecaster during World War II, and after
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See J. Gleick, Chaos: Making a New Science (1987); I. Stewart, Does God Play Dice?: The Mathematics of Chaos (1989); A. A. Tsonis, Chaos: From Theory to Applications (1992); D. N. Chorafas, Chaos Theory in the Financial Markets (1994).

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chaos theory

The theory of the unpredictable behavior that can arise in systems obeying deterministic scientific laws – laws that under ideal conditions completely determine the future states of a system from its preceding states. In practice, however, quantities cannot be measured with unlimited precision and the predictability suffers as a result of input errors. In a typical nonchaotic system, the errors accumulate with time but remain managable. In a chaotic system, there is a sensitivity to variations in the initial conditions. Input errors are multiplied at an escalating rate until all predictive power is lost and the system behaves in an apparently random manner.

There are many apparently simple physical systems in the Universe that obey deterministic laws but yet behave unpredictably.

Collins Dictionary of Astronomy © Market House Books Ltd, 2006

chaos theory

a theory, applied in various branches of science, that apparently random phenomena have underlying order
Collins Discovery Encyclopedia, 1st edition © HarperCollins Publishers 2005
References in periodicals archive ?
Deterministic chaos may turn out to be a more accurate tool for analyzing economic ideas and evidence, too.
The theory of deterministic chaos has challenged our notions of the meaning of the term "random." As Brock and Sayers (1988: 74) point out:
Random-looking variables may in fact be deterministic chaos, and thus, predictable, at least in the short-run.
Usually chaos (deterministic chaos) refers to irregular, unpredictable behavior in deterministic, dissipative, and nonlinear dynamical systems.
In the mid-70s, the term deterministic chaos was introduced by Li and Yorke in a famous paper entitled "Period Three Implies Chaos" [3].
Fatiou, Deterministic chaos, Msc project, University of London, 2005.
For deterministic chaos to exist, a nonlinear dynamical system must have a dense set of periodic orbits and be transitive and sensitive to initial conditions.
In Cao method, at the same time, we use another parameter to distinguish the new good and random signal of the deterministic chaos. That is,
Section I discusses nonlinear dynamics, including the intermittency route to chaos, evolutionary and deterministic chaos, and phase synchronization as well as example systems.
The literature of technology diffusion and market growth has maintained that while deterministic chaos may occur at the beginning or 'end' of an s-shaped market growth curve, the middle section is stable and predictable (Modis and Debecker, 1992, Linstone, 1999).

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