To be useful the prediction has to be able to guide action otherwise it's pointless. If your control variable(s) become state variable(s), for example, you may be within model parameters, as far as variable value assignment, but the modeled has escape the model. And that is IF the differential equations are solvable; a big IF as the majority of 'em ain't.
No amplitude is unlimited, of course, as the dynamic system will self-destruct under continuous positive feedback, when one hooks the emitter to the base of a transistor, or becomes non-dynamic under continuous negative feedback.
