I made an oscillator from the Rossler attractor, which you can also perturb with input:
I am teaching a course on Dynamical Systems this fall; preparing for it is giving me lots of ideas for VCV rack although I can never guarantee I will have the time to execute them.
The book “Elegant Chaos: Algebraically Simple Chaotic Flows” by J.C.Sprott is a great source for these I think, its basically a long list of examples of chaotic attractors with simple definitions, which means all of them would be very feasible to generate at audio rates (although maybe they are more usually useful as LFOs).