Rössler system ($\dot{x}=-y-z,\dot{y}=x+ay,\dot{z}=b+z(x-c)$)

An autonomous differential equation in three variables. Its linear planar rotation couples to a nonlinear vertical variable through $xz$. Depending on parameters, its solutions can approach an equilibrium point, a periodic orbit, or a more complicated attractor. The specialization $b=a$ is used in the 2011 Oxford combined paper.

A chaotic attractor of a Rössler system for suitable parameter values. Local expansion near an unstable spiral combines with excursions in the third coordinate and global return; the existence of a local expanding direction by itself does not prove a chaotic attractor.