# 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 ?
Its state equation (1) (the Lorenz equation) is a simplified model of weather forecasting.
As a deterministic system, the atmospheric dynamical system can be described by a set of Lorenz equations and the slight differences in the initial condition of the Lorenz equation will make the Lorenz equation to show different morphologies in the subsequent motions.
Stenflo, "Generalized Lorenz equations for acoustic-gravity waves in the atmosphere," Physica Scripta, vol.
There have been proposed many hyperchaotic systems, with some designed to facilitate the electronic implementation  and others designed to create certain topologies in the phase space  and, even, new hyperchaotic dynamics have been described to be employed in different encryption schemes , with most of them being based on Lorenz equations [16-18].
Yu, "Bifurcation behavior of the generalized Lorenz equations at large rotation numbers," Journal of Mathematical Physics, vol.
Sparrow, The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors, Springer, New York, NY, USA, 1982.
Maas, "The diffusionless Lorenz equations; Shil'nikov bifurcations and reduction to an explicit map," Physica D, vol.
The study used mathematical equations known as Lorenz equations to calculate how positive and negative human emotions change over time.
Edward Lorenz introduced the first Lorenz equations in 1963 .
Losada uses the same parameter values that are commonly used in models that apply the Lorenz equations. This applies to the parameters a, b and c as well as to parameters that are implicitly considered unity (e.g.

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