A Rössler attractor is a chaotic attracting invariant set occurring in a Rössler system at suitable parameter values. The model was designed to combine continuous-time motion with a folded Poincaré map.[ref]
The distinction between local and global information is essential. An unstable spiral can stretch nearby trajectories apart during one part of an excursion. To sustain bounded irregular motion, the trajectories must also return through the global phase portrait. A local Jacobian matrix describes the stretching near a point; it does not determine where trajectories go after leaving that neighborhood.
Numerically, a useful diagnostic is to record consecutive intersections with a transverse section and plot the resulting Poincaré map. A folded shape suggests how stretching and return interact, but a finite point cloud does not itself prove an invariant set, an attracting neighborhood or a rigorous definition of chaos. The parameter values, section and discarded transient should accompany such a computation.
The Rössler attractor is a chaotic attractor named after the German physicist Otto Rössler, who introduced it in 1976. It is a system of three non-linear ordinary differential equations that model certain dynamical systems, and it is notable for its relatively simple structure compared to other chaotic systems like the Lorenz attractor. The equations that define the Rössler attractor are: 1. \(\frac{dx}{dt} = -y - z\) 2.
New to topics? Read the docs here!