  We show, via numerical simulations, that the fidelity decay behavior of
quasi-integrable systems is strongly dependent on the location of the initial
coherent state with respect to the underlying classical phase space. In
parallel to classical fidelity, the quantum fidelity generally exhibits
Gaussian decay when the perturbation affects the frequency of periodic phase
space orbits and power-law decay when the perturbation changes the shape of the
orbits. For both behaviors the decay rate also depends on initial state
location. The spectrum of the initial states in the eigenbasis of the system
reflects the different fidelity decay behaviors. In addition, states with
initial Gaussian decay exhibit a stage of exponential decay for strong
perturbations. This elicits a surprising phenomenon: a strong perturbation can
induce a higher fidelity than a weak perturbation of the same type.
