chaos theory

Mathematical theory that describes chaotic behavior in a complex system.Applications include the study of turbulent flow in fluids, irregularities in biological systems, population dynamics, chemical reactions, plasma physics, meteorology, the motions of groups and clusters of stars, transportation dynamics, and many other fields.
* * *
▪ mathematics and mechanicsin mechanics and mathematics, the study of apparently random or unpredictable behaviour in systems governed by deterministic laws. A more accurate term, “deterministic chaos,” suggests a paradox because it connects two notions that are familiar and commonly regarded as incompatible. The first is that of randomness or unpredictability, as in the trajectory of a molecule in a gas or in the voting choice of a particular individual from out of a population. In conventional analyses, randomness was considered more apparent than real, arising from ignorance of the many causes at work. In other words, it was commonly believed that the world is unpredictable because it is complicated. The second notion is that of deterministic (determinism) motion, as that of a pendulum or a planet, which has been accepted since the time of Isaac Newton as exemplifying the success of science in rendering predictable that which is initially complex.In recent decades, however, a diversity of systems have been studied that behave unpredictably despite their seeming simplicity and the fact that the forces involved are governed by wellunderstood physical laws. The common element in these systems is a very high degree of sensitivity to initial conditions and to the way in which they are set in motion. For example, the meteorologist Edward Lorenz discovered that a simple model of heat convection possesses intrinsic unpredictability, a circumstance he called the “butterfly effect,” suggesting that the mere flapping of a butterfly's wing can change the weather. A more homely example is the pinball machine: the ball's movements are precisely governed by laws of gravitational rolling and elastic collisions—both fully understood—yet the final outcome is unpredictable.In classical mechanics the behaviour of a dynamical system can be described geometrically as motion on an “attractor.” The mathematics of classical mechanics effectively recognized three types of attractor: single points (characterizing steady states), closed loops (periodic cycles), and tori (combinations of several cycles). In the 1960s a new class of “strange attractors” was discovered by the American mathematician Stephen Smale (Smale, Stephen). On strange attractors the dynamics is chaotic. Later it was recognized that strange attractors have detailed structure on all scales of magnification; a direct result of this recognition was the development of the concept of the fractal (a class of complex geometric shapes that commonly exhibit the property of selfsimilarity), which led in turn to remarkable developments in computer graphics.Applications of the mathematics of chaos are highly diverse, including the study of turbulent flow of fluids, irregularities in heartbeat, population dynamics, chemical reactions, plasma physics, and the motion of groups and clusters of stars.* * *
Universalium. 2010.
Look at other dictionaries:
Chaos Theory — Splinter Cell 3 Soundtrack Soundtrack album to Tom Clancy s Splinter Cell: Chaos Theory by Amon Tobin Released … Wikipedia
chaos theory — Chaos theory is a mathematical theory which describes systems whose behaviour is apparently unpredictable, but which in fact conform to longterm repetitive patterns. Weather is an example of such a system, in that it may seem unpredictable,… … Encyclopedia of contemporary British culture
Chaos Theory — Solicita una imagen para este artículo. Título ¡Vaya caos! Ficha técnica … Wikipedia Español
Chaos Theory (ER) — Chaos Theory ER episode Episode no. Season 9 Episode 1 Directed by Jonathan Kaplan Written by R. Sco … Wikipedia
chaos theory — chaos ,theory noun uncount the scientific study of complicated systems whose behavior is strongly affected by minor changes in conditions … Usage of the words and phrases in modern English
Chaos theory — This article is about chaos theory in Mathematics. For other uses of Chaos theory, see Chaos Theory (disambiguation). For other uses of Chaos, see Chaos (disambiguation). A plot of the Lorenz attractor for values r = 28, σ = 10, b = 8/3 … Wikipedia
Chaos Theory — A mathematical concept that explains that it is possible to get random results from normal equations. The main precept behind this theory is the underlying notion of small occurrences significantly affecting the outcomes of seemingly unrelated… … Investment dictionary
chaos theory — noun : a branch of mathematical and physical theory that deals with the nature and consequences of chaos and chaotic systems • chaos theorist noun * * * ˈchaos theory [chaos theory] noun uncountable … Useful english dictionary
chaos theory — The proposition that a system, although governed by deterministic laws, displays unpredictability owing to sensitivity to changes in independent variables. Chaos in this sense does not refer to the everyday sense of utter confusion. Weather… … Auditor's dictionary
chaos theory — noun Date: 1984 a branch of mathematical and physical theory that deals with the nature and consequences of chaos and chaotic systems … New Collegiate Dictionary