Rössler attractor

State space representation of the Rössler attractor

The Rössler attractor (after Otto E. Rössler ) is a strange attractor that is defined by the following system of differential equations :

{\ displaystyle {\ begin {aligned} {\ dot {X}} & = - (Y + Z) \\ {\ dot {Y}} & = X + aY \\ {\ dot {Z}} & = b + (Xc) Z \ end {aligned}}}

According to Otto Rössler, this model was the observation of a candy - kneading machine ( taffy puller ) on Coney Iceland inspired their toffee repeatedly expands and folds. Unlike the Lorenz attractor , which is derived from the dynamics of convection currents, the Rössler attractor does not describe a real physical system. It is therefore an academic construct that is intended to simply illustrate certain chaotic effects.

properties

The Rössler attractor in the Poincaré map - the z -values rise with increasing x .

The only non-linearity in the system is given by the term in the third coordinate, the other coordinates have only linear terms. The flow on the attractor spirals around an unstable fixed point. However, the outer part of the attractor is injected back into the inner part due to the stronger non-linearity there. Due to the resulting rotation, the attractor has similarities with a Möbius strip . ${\ displaystyle XZ}$

literature

OE Rössler: An Equation for Continuous Chaos . Physics Letters Vol. 57A no 5, pp 397-398, 1976.
OE Rössler: An Equation for Hyperchaos . Physics Letters Vol. 71A no 2,3, pp 155-157, 1979.

Web links

Eric W. Weisstein : Rössler attractor . In: MathWorld (English).
triumf.ca: Rossler Attractors ( Memento from May 23, 2009 in the Internet Archive )