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one of the classic nonlinear 2nd order ODEs is the Duffing equation, which exhibits a supercritical pitchfork: past a certain parameter value, a spiral sink turns to a saddle and sheds a pair of spiral sinks. what's so nice about that? next comes a novel simulation... 1/3
if you add a forcing term, then you can drive the Duffing system to bounce back & forth between the two spiral sinks. i've modelled this as a bead-on-a-wire with two springs in compression, in a shaken box. this is a classic example of a chaotic oscillator, as you'll see... 2/3
i learned about the forced Duffing from Phil Holmes a long time ago, and have seen experiments using deformed beams & lasers -- never seen this model using springs. that's fun. 3/3 for full-quality vids, head over to the youtube channel playlist:
