  We introduce and develop an approach to realizing a topological phase
transition and non-Abelian statistics with dynamically induced Floquet Majorana
Fermions (FMFs). When the periodic driving potential does not break fermion
parity conservation, FMFs can encode quantum information. Quasi-energy analysis
shows that a stable FMF zero mode and two other satellite modes exist in a wide
parameter space with large quasi-energy gaps, which prevents transitions to
other Floquet states under adiabatic driving. We also show that in the
asymptotic limit FMFs preserve non-Abelian statistics and, thus, behave like
their equilibrium counterparts.
