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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] The double-scroll attractor from the Chua circuit was rigorously proven to be chaotic [2] through a number of Poincaré return maps of the attractor explicitly derived by way ...
This animation shows how the attractor of the system changes as the parameter is varied from 0.0 to 1.0 in steps of 0.01. The Ikeda dynamical system is simulated for 500 steps, starting from 20000 randomly placed starting points. The last 20 points of each trajectory are plotted to depict the attractor.
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 values that get close enough to the attractor values ...
The frequency response of this oscillator describes the amplitude of steady state response of the equation (i.e. ()) at a given frequency of excitation . For a linear oscillator with β = 0 , {\displaystyle \beta =0,} the frequency response is also linear.
The Rössler attractor Rössler attractor as a stereogram with =, =, = The Rössler attractor (/ ˈ r ɒ s l ər /) is the attractor for the Rössler system, a system of three non-linear ordinary differential equations originally studied by Otto Rössler in the 1970s.
In attractor networks, an attractor (or attracting set) is a closed subset of states A toward which the system of nodes evolves. A stationary attractor is a state or sets of states where the global dynamics of the network stabilize. Cyclic attractors evolve the network toward a set of states in a limit cycle, which is repeatedly traversed ...
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.
Rössler attractor reconstructed by Takens' theorem, using different delay lengths. Orbits around the attractor have a period between 5.2 and 6.2. In the study of dynamical systems, a delay embedding theorem gives the conditions under which a chaotic dynamical system can be reconstructed from a sequence of observations of the state of that system.