Lorenz attractor


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Lorenz attractor

[′lȯr‚ens ə‚trak·tər]
(physics)
The strange attractor for the solution of a system of three coupled, nonlinear, first-order differential equations that are encountered in the study of Rayleigh-Bénard convection; it is highly layered and has a fractal dimension of 2.06. Also know as Lorenz butterfly.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

Lorenz attractor

(mathematics)
(After Edward Lorenz, its discoverer) A region in the phase space of the solution to certain systems of (non-linear) differential equations. Under certain conditions, the motion of a particle described by such as system will neither converge to a steady state nor diverge to infinity, but will stay in a bounded but chaotically defined region. By chaotic, we mean that the particle's location, while definitely in the attractor, might as well be randomly placed there. That is, the particle appears to move randomly, and yet obeys a deeper order, since is never leaves the attractor.

Lorenz modelled the location of a particle moving subject to atmospheric forces and obtained a certain system of ordinary differential equations. When he solved the system numerically, he found that his particle moved wildly and apparently randomly. After a while, though, he found that while the momentary behaviour of the particle was chaotic, the general pattern of an attractor appeared. In his case, the pattern was the butterfly shaped attractor now known as the Lorenz attractor.
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References in periodicals archive ?
Tucker, "The Lorenz attractor exists," Comptes Rendus de l'Academie des Sciences--Series I-Mathematics, vol.
In the proposed system, the weakly chaotic structures maintain certain similarity with the classic Lorenz attractor (see Figure 10).
Unlike the Lorenz attractor that swiftly exhibits beautiful butterfly wings after a few hundred iterations (Palmer 1993), one further notices in Fig.
Examples of such strange attractors include the famous Lorenz attractor illustrated in Figure 6(d) [30], Henon attractor, and logistic map attractor.
The selected time series chosen to validate the approaches proposed in this paper to estimate [D.sub.2] are the Lorenz attractor, the MIX(P) process, and real HRV signals, respectively.
Yasukochi, "A butterfly-shaped localization set for the Lorenz attractor," Physics Letters A, vol.
Sidorov, "A new view of the Lorenz attractor," Differential Equations, vol.
In addition, MapleSim applies symbolic preprocessing techniques to models created in the Lorenz Attractor. The Lorenz Attractor was created with MapleSim's Signal Blocks and is used to simulate chaotic systems such as climate and weather.
Visualizations of the Mandelbrot Set, the Lorenz Attractor and the Feigenbaum function in the complex plane are stunning and rival many renditions of what are considered more conventional art forms.
The "Lorenz attractor" was discovered when Lorenz mapped the points created during his study of meteorological data.
Through something that's called phase graphing in chaos theory, we see systems fluctuate wildly over time, but then, phase graphing shows systems being "attracted to a fixed point" (Gleick, 1987, pp.233-36) Sometimes this has been called the Lorenz attractor. The attractor is basically a region within a dynamic system to which the system is drawn.