Search results
Results from the WOW.Com Content Network
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.
Main page; Contents; Current events; Random article; About Wikipedia; Contact us; Pages for logged out editors learn more
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 ...
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
For r < 1, exists outside [0, 1] as an unstable fixed point, but for r = 1, the two fixed points collide, and for r > 1, appears between [0, 1] as a stable fixed point. When the parameter r = 1, the trajectory of the logistic map converges to 0 as before, but the convergence speed is slower at r = 1.
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.
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 ...