Rössler attractor

Knowing that the Rössler attractor can be used to create a pseudo 1-d map, it then follows to use similar analysis methods.

The blue line corresponds to the standard Rössler attractor generated with , , and .

Bifurcation diagrams are a common tool for analyzing the behavior of dynamical systems, of which the Rössler attractor is one.

The banding evident in the Rössler attractor is similar to a Cantor set rotated about its midpoint.

Additionally, the half-twist that occurs in the Rössler attractor only affects a part of the attractor.

Rössler attractor's behavior is largely a factor of the values of its constant parameters , , and .

Otto Rössler designed the Rössler attractor in 1976, but the originally theoretical equations were later found to be useful in modeling equilibrium in chemical reactions.

The original Rössler paper states the Rössler attractor was intended to behave similarly to the Lorenz attractor, but also be easier to analyze qualitatively.

In the case of the Rössler attractor, the plane is uninteresting, as the map always crosses the plane at due to the nature of the Rössler equations.

This should not be surprising, considering that nonlinear autonomous systems in three dimensions can produce truly chaotic behavior such as the Lorenz attractor and the Rössler attractor.

Except in those cases where the initial conditions lie on the attracting plane generated by and , this influence effectively involves pushing the resulting system towards the general Rössler attractor.

Examples of strange attractors include the Double-scroll attractor, Hénon attractor, Rössler attractor, and the Lorenz attractor.

His most heavily-cited publication is the 1976 paper in which he studied what is now known as the Rössler attractor, a system of three linked differential equations that exhibit chaotic dynamics.

Otto Eberhard Rössler (born 20 May 1940) is a German biochemist known for his work on chaos theory and the theoretical equation known as the Rössler attractor.

As shown in the general plots of the Rössler Attractor above, one of these fixed points resides in the center of the attractor loop and the other lies comparatively removed from the attractor.

Although these eigenvalues and eigenvectors exist in the Rössler attractor, their influence is confined to iterations of the Rössler system whose initial conditions are in the general vicinity of this outlier fixed point.

Note that the magenta line nearly touches the plane of the attractor before being pulled upwards into the fixed point; this suggests that the general appearance and behavior of the Rössler attractor is largely a product of the interaction between the attracting and the repelling and plane.