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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 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 ...
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.
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.
The critical attractor. An attractor is a term used to refer to a region that has the property of attracting surrounding orbits, and is the orbit that is eventually drawn into and continues. The attractive fixed points and periodic points mentioned above are also members of the attractor family.
As I understand it from my math undergrad days, this is the Lorenz attractor. Debivort 03:13, 27 December 2005 (UTC) Veledan, read the attractor article first. If you understand the concept of attractor, it shouldn't be hard to understand main surprise of Lorenz attractor, and meaning of the picture. It's not esotheric at all, its simply kind ...
The system indeed appears to exhibit a great dependence on initial conditions, a defining property of chaotic systems; moreover, two attractors of the system are seen in both plots. The Malkus waterwheel , also referred to as the Lorenz waterwheel or chaotic waterwheel , [ 1 ] is a mechanical model that exhibits chaotic dynamics.