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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.
A plot of Lorenz' strange attractor for values ρ=28, σ = 10, β = 8/3. The butterfly effect or sensitive dependence on initial conditions is the property of a dynamical system that, starting from any of various arbitrarily close alternative initial conditions on the attractor, the iterated points will become arbitrarily spread out from each other.
In the case of the logistic map with parameter r = 4 and an initial state in (0,1), the attractor is also the interval (0,1) and the probability measure corresponds to the beta distribution with parameters a = 0.5 and b = 0.5. Specifically, [22] the invariant measure is ().
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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
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 ...
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 ...