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.

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.
References in periodicals archive ?
In fact, the motivation of Lorenz system approach has been mentioned in the author's past papers in this field.
Through this paper, we show robustness and efficiency of the method via a number of examples including the chaotic Lorenz system [25] and the NLSE.
In order to validate the efficiency and effectiveness of the proposed theory, the complex Lorenz system, the complex Chen system, the complex Lu system, and Rossler system with disturbance are proposed and corresponding controllers are designed.
Some researchers added the memristor model to Chua's circuit [13], and others combined the Lorenz system with memristors [14].
In the above discussed literature, the given systems usually were typical benchmark chaotic systems, such as the Lorenz system, Chen system, and Lii system.
[3] Jian Zhang, An Image Encryption Scheme Based on Cat Map and Hyperchaotic Lorenz System. International Conference on Computational Intelligence & Communication Technology.
He, "Characteristic analysis and DSP realization of fractional-order simplified Lorenz system based on Adomian decomposition method," International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol.
The Lorenz system has been extensively employed: cyphers [2, 3], circuits [4], engineered systems [5], and so forth have been based on this dynamics.
In this section, in order to discuss the influence of the time series on the estimation accuracy, we consider a Lorenz system.
Kokubu and Roussarie [5] established the existence of a singularly degenerate heteroclinic cycle in the Lorenz system and some of its other dynamical consequences.
The discovery of the eminent Lorenz system [1] has led to an extensive study of chaotic behaviors in nonlinear systems due to many possible applications in science and technology In the last three decades, many new three-dimension chaotic systems have been proposed, such as Rossler system [2], Chen and Ueta system [3], Lu and Chen system [4], Liu et al.