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).

chaos theory A set of mathematical models according to which simple equations and initial conditions give rise to complicated paths for variables. Some of these models have been applied to financial markets.