The stability of Majorana fermions at the edges of a two-dimensional topological superconductor after a quantum quench is studied. Both instantaneous and slow quenches are considered. In the case of instantaneous quenches, the Majorana modes generally decay, but for a finite system there is a revival time that scales to infinity as the system size grows. Exceptions to this decaying behavior are found in some cases such as due to the presence of edge states with the same momentum in the final state. It is shown that the Chern number remains invariant after the quench, until the propagation of the mode along the transverse direction reaches the middle point.

A periodic driving is also considered. In this work we consider triplet and singlet superconductors subject to periodic variations of the chemical potential, spin-orbit coupling and magnetization in both topologically trivial and nontrivial phases, and study their influence on the charge and spin currents that propagate along the edges of the two-dimensional system.