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The Lorenz attractor is an iconic example of a strange attractor in chaos theory.This three-dimensional fractal structure, resembling a butterfly or figure eight, reflects the long-term behavior of solutions to the Lorenz system, a set of three differential equations used by mathematician and meteorologist Edward N. Lorenz as a simple description of fluid circulation in a shallow layer (of ...
In particular, the Lorenz attractor is a set of chaotic solutions of the Lorenz system. The term " butterfly effect " in popular media may stem from the real-world implications of the Lorenz attractor, namely that tiny changes in initial conditions evolve to completely different trajectories .
Burke-Shaw chaotic attractor [8] continuous: real: 3: 2: Chen chaotic attractor [9] continuous: real: 3: 3: Not topologically conjugate to the Lorenz attractor. Chen-Celikovsky system [10] continuous: real: 3 "Generalized Lorenz canonical form of chaotic systems" Chen-LU system [11] continuous: real: 3: 3: Interpolates between Lorenz-like and ...
The Lorenz attractor is a 3-dimensional structure corresponding to the long-term behavior of a chaotic flow, noted for its butterfly shape. The map shows how the state of a dynamical system (the three variables of a three-dimensional system) evolves over time in a complex, non-repeating pattern.
Print/export Download as PDF; Printable version; In other projects ... The Lorenz 96 model is a dynamical system formulated by Edward Lorenz in 1996. [1] It is ...
The Malkus waterwheel, also referred to as the Lorenz waterwheel or chaotic waterwheel, [1] is a mechanical model that exhibits chaotic dynamics. Its motion is governed by the Lorenz equations. While classical waterwheels rotate in one direction at a constant speed, the Malkus waterwheel exhibits chaotic motion where its rotation will speed up ...
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Visual representation of a strange attractor. [1] Another visualization of the same 3D attractor is this video.Code capable of rendering this is available.. In the mathematical field of dynamical systems, an attractor is a set of states toward which a system tends to evolve, [2] for a wide variety of starting conditions of the system.