  We show the localization transition and its effect on two dynamical processes
for an extended Aubry-Andr\'e-Harper model with incommensurate on-site and
hopping potentials. After specifying an extended Aubry-Andr\'e-Harper model, we
check the localization transition for all the eigenstates and eigenenergy band
splitting behavior versus a system parameter. To examine the effect of
localization transition on dynamical processes, firstly, the slowly pumping of
the edge states are examined. In the dynamical processes, the system acts as
conductor for the excitation in the nonlocal region and insulator in the
localized region. Then by quantum Lyapunov control method with different
control Hamiltonians, we prepare an edge localized state which exists in the
nonlocal region. Compared to that in the nonlocal region, the control effect is
suppressed in the localized region. Then we employ the entropy and occupation
imbalance between even and odd sites to indicate the localization transition
further. Finally, the experimental schemes based on cold atoms trapped
quasiperiodic optical lattice and coupled optical waveguide arrays are
suggested.
