# chaos theory

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## chaos theory

**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 dynamics). Some of the early investigators of chaos were the American physicist Mitchell Feigenbaum; the Polish-born mathematician and inventor of fractals (see fractal geometry) Benoit Mandelbrot; the American mathematician James Yorke, who popularized the term “chaos”; and the American meteorologist Edward Lorenz.

### Bibliography

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