chaos theory

(redirected from Non-linear dynamics)
Also found in: Dictionary, Medical, Financial.

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).
..... Click the link for more information.
). 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.
..... Click the link for more information.
) 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
..... Click the link for more information.
; 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
..... Click the link for more information.
.

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

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.

chaos theory

a theory, applied in various branches of science, that apparently random phenomena have underlying order
References in periodicals archive ?
Non-linear dynamics of gear-pair systems with periodic stiffness and backlash, Journal of Sound and Vibration 229(2): 287-310.
This article illustrates the non-linear resiliency origin, then discusses the non-linear dynamics model unity for the above-mentioned two kinds of relative rotation dynamics system under the non-linear resiliency and finally applies chaos system analysis theory to reveal unified system chaos movement performance under the influence of weak cyclical disturbing force.
Others of the 65 papers consider such aspects as optical techniques, plates and composites, and non-linear dynamics.
Among the themes that emerge from the papers are need to go beyond Malthusian analysis in linking social violence and natural resource use, the inadequacy of economistic approaches to what the non-linear dynamics between nature and humanity, and the contributions of critical theory to the building of international ecopolitical theory.
Dankowicz is conducting research into non-linear dynamics.
The main goal of this work was to look for the presence of non-linear dynamics and deterministic chaos in those systems and quantitative characterization of some chaotic parameters (phase space dimension, attractor dimension), essential for determining how much fracturing and destruction processes are similar in various scales.
Non-linear dynamics uses unconventional ways of thinking to look for patterns in large quantities of data.
62), calls the research ideology and practice relating to non-linear dynamics and complexity theories "dynamical literacy.
But here's a second opinion: it is the conjunction of the choice of unit observable and the allegiance to universal linear dynamics that leads to the measurement problem; we can privilege the identity and avert the problem by invoking non-linear dynamics - von Neumann's measurement collapses.
The latest trend in non-linear dynamics, complexity theory is best explained by the concept of convection.
Because it has parameters that can be directly related to nature, and for which meaningful values can be assigned through the work of Yodzis and Innes (1992), the model of Hastings and Powell (1991) is likely to find many further uses as a test-bed for investigations into chaos and non-linear dynamics.

Full browser ?