What does it mean for a dynamical system to be well-behaved?
I'm not sure there's a concrete definition.  I find it mildly amusing that it's in a neural net paper, because it's one of those common sense things that can't easily be encoded for AI, with or without neural nets.

Mostly I'd call a system "well behaved" if I could get it to do what I need it to do without pulling my hair out.  But if I had to give it criteria I'd probably consider a dynamic system to be well behaved if it is stable or easily stabilizable, if it doesn't have any strong resonances that can't easily be damped, and if it isn't too "stiff"; i.e. if the Jacobian of $f(x)$ doesn't change greatly as x is varied (or even more formally, if the Hessian of $f(x)$ isn't too big).