Sabbatical trip to Europe – Part 3 (Otto Rössler)

After the conference in Switzerland, I stopped in Tübingen, Germany to visit Otto Rössler. Nearly everyone who learned about nonlinear systems knows the nowadays named Rössler attractor and his work in chaos theory in the 1970s.
For the last four years we were in contact for my science history project and this year, I finally visited him. We had a great day and I received MANY documents from conferences 40-50 years ago. He saved ‘everything’ in countless binders, sorted by years, and kept them in ceiling-heigh bookshelfs at his home.

In the 1970s, Otto Rössler designed a famous 3D flow that mimics the folding and bending of taffy in a taffy machine, which is now named the Rössler attractor. Described by the 3 coupled differential equations

\begin{aligned}\dot x &= -y – z, \\ \dot y &= x + a y,\\ \dot z &= b – c z + x z,\end{aligned}

with just one nonlinear term, the x z in the third equation. The Rössler velocity field results from the interaction of two crossed vortices, one near the origin and the other far away pointing at the “fold” in the Rössler band. The parameter space \{a,b,c\} is large, but the system undergoes a period-doubling route to chaos in \{0<a<2, b=2, c=4\}, as in the animation below, which culminates in a period-3 window.

The animation was created by John Lindner.