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The phase space is the horizontal complex plane; the vertical axis measures the frequency with which points in the complex plane are visited. The point in the complex plane directly below the peak frequency is the fixed point attractor. A fixed point of a function or transformation is a point that is mapped to itself by the function or ...
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. [1] [2] These differential equations define a continuous-time dynamical system that exhibits chaotic dynamics associated with the fractal properties ...
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.
An attractor is a stable point which is also called a "sink". The repeller is considered as an unstable point, which is also known as a "source". A phase portrait graph of a dynamical system depicts the system's trajectories (with arrows) and stable steady states (with dots) and unstable steady states (with circles) in a phase space.
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.
Hubble Space Telescope image showing part of the Norma cluster, including ESO 137-002. The Great Attractor is a region of gravitational attraction in intergalactic space and the apparent central gravitational point of the Laniakea Supercluster of galaxies that includes the Milky Way galaxy, as well as about 100,000 other galaxies.
Thomas' cyclically symmetric attractor. In the dynamical systems theory , Thomas' cyclically symmetric attractor is a 3D strange attractor originally proposed by René Thomas . [ 1 ] It has a simple form which is cyclically symmetric in the x, y, and z variables and can be viewed as the trajectory of a frictionally dampened particle moving in a ...
The dipole repeller is directly opposed to the Shapley Attractor, an over-density of galaxies located in the Shapley Supercluster. The dipole repeller's apparent repulsion is due to matter in the vicinity being pulled towards the Shapley Attractor, along with the Great Attractor. Due to this, the dipole repeller has likely become devoid of ...