We have developed a model of the response of the outer Oort cloud of comets to simultaneous tidal perturbations of the adiabatic galactic force and a stellar impulse. The six-dimensional phase space of near-parabolic comet orbital elements has been subdivided into cells. A mapping of the evolution of these elements from beyond the loss cylinder boundary into the inner planetary region over the course of a single orbit is possible. This is done by treating each perturbation separately, and in combination, during a time interval of 5 Myr. We then obtain the time dependence of a wide range of observable comet flux characteristics, which provides a fingerprint of the dynamics. These include the flux distributions of energy, perihelion distance, major axis orientation, and angular momentum orientation. Correlations between these variables are also determined. We show that substantive errors occur if one superposes the separately obtained flux results of the galactic tide and the stellar impulse rather than superposing the tidal and impulsive perturbations in a single analysis. Detailed illustrations are given for an example case where the stellar mass and relative velocity have the ratio M /V rel = 0.043 M /km s -1 and the solar impact parameter is 45,000 AU. This case has features similar to the impending Gliese 710 impulse with the impact parameter selected to be close to the low end of the predicted range. We find that the peak in the observable comet flux exceeds that due to the galactic tide alone by β41%. We also present results for the time dependence of the flux enhancements and for the mean encounter frequency of weak stellar impulse events as functions of M /V rel and solar impact parameter.