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A double-scroll Chen attractor from a simulation. In the mathematics of dynamical systems, the double-scroll attractor (sometimes known as Chua's attractor) is a strange attractor observed from a physical electronic chaotic circuit (generally, Chua's circuit) with a single nonlinear resistor (see Chua's diode).
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]
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.
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.
Two hidden chaotic attractors and one hidden periodic attractor coexist with two trivial attractors in Chua circuit (from the IJBC cover [9]). The classical implementation of Chua circuit is switched on at the zero initial data, thus a conjecture was that the chaotic behavior is possible only in the case of unstable zero equilibrium. [5]
Tinkerbell attractor with a=0.9, b=-0.6013, c=2, d=0.5. Used starting values of = and =.. The Tinkerbell map is a discrete-time dynamical system given by: + = + + + = + + Some commonly used values of a, b, c, and d are
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.
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.