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This chaotic attractor is known as the double scroll because of its shape in three-dimensional space, which is similar to two saturn-like rings connected by swirling lines. The attractor was first observed in simulations, then realized physically after Leon Chua invented the autonomous chaotic circuit which became known as Chua's circuit. [1]
He is known for the Chen attractor, Lu Chen attractor, and other works on Multiscroll attractors. He conducts research on chaos, control theory, bifurcations, nonlinear dynamics, complex systems, etc. [2]
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.
Floris Takens (12 November 1940 – 20 June 2010) [1] was a Dutch mathematician known for contributions to the theory of chaotic dynamical systems.. Together with David Ruelle, he predicted that fluid turbulence could develop through a strange attractor, a term they coined, as opposed to the then-prevailing theory of accretion of modes.
Michel Hénon (French:; 23 July 1931, Paris – 7 April 2013, Nice) was a French mathematician and astronomer. [1] He worked for a long time at the Nice Observatory.. In astronomy, Hénon is well known for his contributions to stellar dynamics.
Zaslavskii map with parameters: =, =, =. The Zaslavskii map is a discrete-time dynamical system introduced by George M. Zaslavsky.It is an example of a dynamical system that exhibits chaotic behavior.
The Hénon attractor is a fractal, smooth in one direction and a Cantor set in another. Numerical estimates yield a correlation dimension of 1.21 ± 0.01 or 1.25 ± 0.02 [2] (depending on the dimension of the embedding space) and a Box Counting dimension of 1.261 ± 0.003 [3] for the attractor of the classical map.
Plot of the Duffing map showing chaotic behavior, where a = 2.75 and b = 0.15. Phase portrait of a two-well Duffing oscillator (a differential equation, rather than a map) showing chaotic behavior.