When I saw the title of the thread the first thing I thought of was analog computers that model a system of diff. eqs with another physical system that’s easier to manipulate—faster, smaller or what have you. Because otherwise, everything is software!
Someone brought up the Aalto waveguide. You could do an analog hardware version of this, but it might be tricky. A saturation in the loop allows feedback to not blow up, and is responsible for the harmonics generated. It’s asymmetrical around 0 in a very specific way that would not be straightforward to construct as a stable analog circuit. With this and a very high quality digital delay you’d have a really fun waveguide module though so it might be worth doing.