  Bifurcations are one of the most remarkable features of dynamical systems.
Corral et al. [Sci. Rep. 8(11783), 2018] showed the existence of scaling laws
describing the transient (finite-time) dynamics in discrete dynamical systems
close to a bifurcation point, following an approach that was valid for the
transcritical as well as for the saddle-node bifurcations. We reformulate those
previous results and extend them to other discrete and continuous bifurcations,
remarkably the pitchfork bifurcation. In contrast to the previous work, we
obtain a finite-time bifurcation diagram directly from the scaling law, without
a necessary knowledge of the stable fixed point. The derived scaling laws
provide a very good and universal description of the transient behavior of the
systems for long times and close to the bifurcation points.
