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 regionin the phase space of the solution to certain systems of(non-linear) differential equations. Under certainconditions, the motion of a particle described by such assystem will neither converge to a steady state nor diverge toinfinity, but will stay in a bounded but chaotically definedregion. By chaotic, we mean that the particle's location,while definitely in the attractor, might as well be randomlyplaced there. That is, the particle appears to move randomly,and yet obeys a deeper order, since is never leaves theattractor.

Lorenz modelled the location of a particle moving subject toatmospheric forces and obtained a certain system of ordinary differential equations. When he solved the systemnumerically, he found that his particle moved wildly andapparently randomly. After a while, though, he found thatwhile the momentary behaviour of the particle was chaotic, thegeneral pattern of an attractor appeared. In his case, thepattern was the butterfly shaped attractor now known as theLorenz attractor.

单词	lorenz attractor
释义	Lorenz attractor 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 regionin the phase space of the solution to certain systems of(non-linear) differential equations. Under certainconditions, the motion of a particle described by such assystem will neither converge to a steady state nor diverge toinfinity, but will stay in a bounded but chaotically definedregion. By chaotic, we mean that the particle's location,while definitely in the attractor, might as well be randomlyplaced there. That is, the particle appears to move randomly,and yet obeys a deeper order, since is never leaves theattractor. Lorenz modelled the location of a particle moving subject toatmospheric forces and obtained a certain system of ordinary differential equations. When he solved the systemnumerically, he found that his particle moved wildly andapparently randomly. After a while, though, he found thatwhile the momentary behaviour of the particle was chaotic, thegeneral pattern of an attractor appeared. In his case, thepattern was the butterfly shaped attractor now known as theLorenz attractor.
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