This study investigates the development of the polar cap area as simulated by global magnetohydrodynamic models of the Earth's magnetosphere during the 14--16 July 2000 (Bastille Day) event. Around 1440 UT on 15 July, a magnetic cloud hit the magnetosphere and in the following hours high levels of activity in the magnetosphere and ionosphere were driven by the frequent changes in solar wind conditions. We compare the size of the polar cap (region of open magnetic field lines) as computed with two MHD models (UCLA-GGCM and BATSRUS) with observation data obtained from the IMAGE and Polar satellites. The two models in general reproduce the changes of the polar cap size that are seen by the satellite imagers. The range of modeled polar cap sizes, however, is limited to about 50--80% of the size range seen by the imagers and the shapes of the polar caps sometimes differ considerably among the models and compared to the observations. We found that a smoothing of solar wind parameters occurs, suggesting that solar wind inputs are stored in the magnetospheric system over a certain memory timescale. Cross-correlations are computed between smoothed solar wind input and the time history of the resulting polar cap size. Modeled magnetospheric memory timescales are estimated to be less than 12 min, whereas the satellite image data suggest a timescale of more than 20 min. The driver of magnetospheric activity in the models was found to be the Bz (north-south) component of the solar wind magnetic field and to a lesser degree, the Akasofu $epsilon$ parameter which is closely related to Bz but is also influenced by the solar wind velocity Vx and magnetic field By. N, Vx, and Pdyn $propto$ NVx2 show some degree of anticorrelation with observed polar cap sizes, but anticorrelations are barely significant for polar caps computed from either model. Memory timescales and reaction time delays could be derived from some of the parameters within the limits of statistical significance of the correlation coefficients.