We have explored the non-locality of two qubits interacting time-dependently with a
nondegenerate parametric amplifier cavity fields in the presence of the Stark shift interaction term. The time-dependent two-qubit reduced density matrix is calculated numerically when the cavity fields are initially in two entangled coherent states. We investigate the non-locality via local Fisher information and negativity. It is shown that the generated non-locality depends on the time-dependent two-qubit location, the Stark shift interaction, the difference between the mean photon numbers of the two-cavity fields as well as the initial intensity coherent fields. The agreement of the generated correlations presented by the local Fisher information and the negativity depends on the
physical parameters. The Stark shift non-linearity and the difference between the mean photon numbers lead to reducing the generated correlations. The local Fisher information is more robust against the Stark shift interaction than the negativity.