1976 The Rössler system

The system

The most popular example of the a simple folding remains the Rössler system proposed in 1976 [1] :

It is characterized by a first-return map with a differentiable critical point separating the increasing and decreasing branches. The Rössler attractor is observed with parameter values \(a=0.420\), \(b=2\) and \(c=4\).

(a) Folded chaos solution to the Rössler system.

(b) First-return map to a Poincaré section.

Fig. 1 : Spiral chaos solution to the Rössler system.

Rössler called this simple stretched and folded ribbon, the spiral chaos. He already sketch the structure of the attractor with a paper model as shown in Fig. 2 [2].

For other parameter values, a more developed chaos is produced. The first-return map to a Poincaré section has now many monotonic branches as shown in Fig. 3. Rössler named that type of chaos, the funnel chaos. Its topology has been investigated by Letellier et al [3]. The spiral chaotic attractor corresponds to a phase coherent attractor while the funnel type is phase incoherent [4].