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A sample solution in the Lorenz attractor when ρ = 28, σ = 10, and β = 8 / 3 . The Lorenz system is a system of ordinary differential equations first studied by mathematician and meteorologist Edward Lorenz.
In mathematics, a chaotic map is a map (an evolution function) that exhibits some sort of chaotic behavior.Maps may be parameterized by a discrete-time or a continuous-time parameter.
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 ...
750 × 750 (1.78 MB) Wikimol: 17:45, 4 January 2006: 750 × 750 (1.8 MB) Wikimol: An icon of chaos theory - the Lorenz atractor. Now in SVG. Projection of trajectory of Lorenz system in phase space Based on images Image:Lorenz system r28 s10 b2-6666.png by User:Wikimol and Image:Lorenz attractor.svg by [[User:User:Dschw
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Lorenz equations used to generate plots for the y variable. The initial conditions for x and z were kept the same but those for y were changed between 1.001, 1.0001 and 1.00001. The values for , and were 45.91, 16 and 4 respectively. As can be seen from the graph, even the slightest difference in initial values causes significant changes after ...
An attractor is a stable point which is also called a "sink". The repeller is considered as an unstable point, which is also known as a "source". A phase portrait graph of a dynamical system depicts the system's trajectories (with arrows) and stable steady states (with dots) and unstable steady states (with circles) in a phase space.
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. System ...