In the movie the control system appears to be a tower of Macs and SG computers.
JP was filmed in 1992 and came out in '93, so this would be OS 9 (?) - DK, I bought my first Mac in 2008.
"The crew filmed scenes for the Park's labs and control room, which used animations for the computers lent by Silicon Graphics and Apple." (Wikipedia).
(I noticed this a few weeks ago when we watched the movie. Very well done if a bit cheesy in places.)