Dynamic models most of the time involve differential equations, which are "time-local". Such models can also be considered "globally", that is in the sense of "trajectories" in the "space-time" state. Up to adapted concepts, such a different interpretation reveals itself more flexible, namely because it allows to use Various operatorial transformations whose time-local equivalent in general cannot exist and from which can result some remarkable properties. Namely, we introduce a principle of parametrizing for dynamic equations by means of such transformations. We then consider an example of bioreactor model for which we highlight how suitable time-nonlocal transformations can sometimes be used to efficiently solve some nonlinear control problems.