Lorenz attractor - определение. Что такое Lorenz attractor
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Что (кто) такое Lorenz attractor - определение

SYSTEM OF ORDINARY DIFFERENTIAL EQUATIONS FIRST STUDIED BY EDWARD LORENZ
Lorenz attractor; Lorentz attractor; Lorenz Attractor; Lorenz's attractor; Lorentz's attractor; Lorenz equation; Lorenz equations; Lorentz system; Lorenz oscillator; Smale's fourteenth problem; Butterfly attractor; Lorenz's strange attractor
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Найдено результатов: 130
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. (1996-01-13)
Lorenz system         
The Lorenz system is a system of ordinary differential equations first studied by mathematician and meteorologist Edward Lorenz. It is notable for having chaotic solutions for certain parameter values and initial conditions.
Lorenz Beven         
ANGLICAN ARCHDEACON
Francis Lorenz Beven; Lorenz Bevan
Francis Lorenz Bevan, MA (30 October 1872“Alumni Cantabrigienses: A Biographical List of All Known Students, Volume 2” Venn, J/Venn, J.A: Cambridge, CUP 1902 (rev 1940, 2011) – 11 March 1947 Rootsweb) was an Anglican priest in Sri Lanka during the first half of the Twentieth century:World Cat he was the Archdeacon of Jaffna from 1925 until 1935; and after that Archdeacon of Colombo from then until his death.
Lorenz Leonard Lindelöf         
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FINNISH MATHEMATICIAN AND ASTRONOMER (1827–1908)
Leonard Lorenz Lindelöf; Lorenz Lindelöf; Lorenz Leonard Lindelof
Lorenz Leonard Lindelöf (13 November 1827, Karvia, Finland – 3 March 1908, Helsinki) was a Finnish mathematician and astronomer.
Lorenz Nikolai Achté         
  • Lorenz Nikolai Achté.
FINNISH OPERA SINGER, COMPOSER, CONDUCTOR AND MUSIC TEACHER (1835-1900)
Lorenz Nikolai Achte; Lorenz Nicolai Achté
Lorenz Nikolai Achté (25 May 1835 – April 18, 1900) was a Finnish opera singer, composer, conductor and music teacher. He was born in Pori, and was one of the Finnish Opera's first artists, together with his wife Emmy Achté.
strange attractor         
  • Weakly attracting fixed point for a complex number evolving according to a [[complex quadratic polynomial]]. The phase space is the horizontal complex plane; the vertical axis measures the frequency with which points in the complex plane are visited. The point in the complex plane directly below the peak frequency is the fixed point attractor.
  • iterates]] the function ''f''(''z'')&nbsp;=&nbsp;''z''<sup>2</sup>&nbsp;+&nbsp;''c''. The three darkest points are the points of the 3-cycle, which lead to each other in sequence, and iteration from any point in the basin of attraction leads to (usually asymptotic) convergence to this sequence of three points.
  • bifurcation]] appears around <math>r\approx3.0</math>, a second bifurcation (leading to four attractor values) around <math>r\approx3.5</math>. The behaviour is increasingly complicated for <math>r>3.6</math>, interspersed with regions of simpler behaviour (white stripes).
  • A plot of [[Lorenz's strange attractor]] for values&nbsp;''ρ''&nbsp;=&nbsp;28,&nbsp;''σ''&nbsp;=&nbsp;10,&nbsp;''β''&nbsp;=&nbsp;8/3
  • Van der Pol]] [[phase portrait]]: an attracting limit cycle}}
SET OF NUMERICAL VALUES TOWARD WHICH A SYSTEM TENDS TO EVOLVE, FOR A WIDE VARIETY OF STARTING CONDITIONS OF THE SYSTEM
Strange attractor; Point attractor; Periodic attractor; Periodic point attractor; Chaotic attractor; Attraction basin; Basin of attraction; Basins of attraction; Stable attractor; Attractor basin; Repellor; Attractor set; Strange attractors
¦ noun Mathematics a complex pattern of behaviour displayed by a chaotic system.
František Lorenz         
CZECH-BORN PHILOSOPHER AND ESPERANTIST (1872-1957)
František Lorentz; Frantisek Lorentz; Frantisek Lorenz; František Lorenc
František Vladimír Lorenc (24 December 1872 – 24 May 1957), known in Portuguese as Francisco Valdomiro Lorenz, was a Czech-born polyglot and philosopher born in Zbyslav (nowadays part of the Czech Republic). He was one of the first Esperantists in the world, and was able to communicate in over 100 different languages.
Attractor         
  • Weakly attracting fixed point for a complex number evolving according to a [[complex quadratic polynomial]]. The phase space is the horizontal complex plane; the vertical axis measures the frequency with which points in the complex plane are visited. The point in the complex plane directly below the peak frequency is the fixed point attractor.
  • iterates]] the function ''f''(''z'')&nbsp;=&nbsp;''z''<sup>2</sup>&nbsp;+&nbsp;''c''. The three darkest points are the points of the 3-cycle, which lead to each other in sequence, and iteration from any point in the basin of attraction leads to (usually asymptotic) convergence to this sequence of three points.
  • bifurcation]] appears around <math>r\approx3.0</math>, a second bifurcation (leading to four attractor values) around <math>r\approx3.5</math>. The behaviour is increasingly complicated for <math>r>3.6</math>, interspersed with regions of simpler behaviour (white stripes).
  • A plot of [[Lorenz's strange attractor]] for values&nbsp;''ρ''&nbsp;=&nbsp;28,&nbsp;''σ''&nbsp;=&nbsp;10,&nbsp;''β''&nbsp;=&nbsp;8/3
  • Van der Pol]] [[phase portrait]]: an attracting limit cycle}}
SET OF NUMERICAL VALUES TOWARD WHICH A SYSTEM TENDS TO EVOLVE, FOR A WIDE VARIETY OF STARTING CONDITIONS OF THE SYSTEM
Strange attractor; Point attractor; Periodic attractor; Periodic point attractor; Chaotic attractor; Attraction basin; Basin of attraction; Basins of attraction; Stable attractor; Attractor basin; Repellor; Attractor set; Strange attractors
·noun One who, or that which, attracts.
Attractor         
  • Weakly attracting fixed point for a complex number evolving according to a [[complex quadratic polynomial]]. The phase space is the horizontal complex plane; the vertical axis measures the frequency with which points in the complex plane are visited. The point in the complex plane directly below the peak frequency is the fixed point attractor.
  • iterates]] the function ''f''(''z'')&nbsp;=&nbsp;''z''<sup>2</sup>&nbsp;+&nbsp;''c''. The three darkest points are the points of the 3-cycle, which lead to each other in sequence, and iteration from any point in the basin of attraction leads to (usually asymptotic) convergence to this sequence of three points.
  • bifurcation]] appears around <math>r\approx3.0</math>, a second bifurcation (leading to four attractor values) around <math>r\approx3.5</math>. The behaviour is increasingly complicated for <math>r>3.6</math>, interspersed with regions of simpler behaviour (white stripes).
  • A plot of [[Lorenz's strange attractor]] for values&nbsp;''ρ''&nbsp;=&nbsp;28,&nbsp;''σ''&nbsp;=&nbsp;10,&nbsp;''β''&nbsp;=&nbsp;8/3
  • Van der Pol]] [[phase portrait]]: an attracting limit cycle}}
SET OF NUMERICAL VALUES TOWARD WHICH A SYSTEM TENDS TO EVOLVE, FOR A WIDE VARIETY OF STARTING CONDITIONS OF THE SYSTEM
Strange attractor; Point attractor; Periodic attractor; Periodic point attractor; Chaotic attractor; Attraction basin; Basin of attraction; Basins of attraction; Stable attractor; Attractor basin; Repellor; Attractor set; Strange attractors
In the mathematical field of dynamical systems, an attractor is a set of states toward which a system tends to evolve, for a wide variety of starting conditions of the system. System values that get close enough to the attractor values remain close even if slightly disturbed.
Lorenz E. Zimmerman         
AMERICAN UNIVERSITY TEACHER (1920-2013)
Lorenz Zimmerman
Lorenz Eugene Zimmerman (November 15, 1920 – March 16, 2013)biographical information: American Men & Women of Science. A biographical directory of today's leaders in physical, biological and related sciences.

Википедия

Lorenz system

The Lorenz system is a system of ordinary differential equations first studied by mathematician and meteorologist Edward Lorenz. It is notable for having chaotic solutions for certain parameter values and initial conditions. In particular, the Lorenz attractor is a set of chaotic solutions of the Lorenz system. In popular media the "butterfly effect" stems from the real-world implications of the Lorenz attractor, namely that in a chaotic physical system, in the absence of perfect knowledge of the initial conditions (even the minuscule disturbance of the air due to a butterfly flapping its wings), our ability to predict its future course will always fail. This underscores that physical systems can be completely deterministic and yet still be inherently unpredictable. The shape of the Lorenz attractor itself, when plotted in phase space, may also be seen to resemble a butterfly.