Klein-Gordon-Schroedinger(KGS)equationsareveryimportantinphysics.Somepapersstudiedtheirwell-posednessandnumericalsolution[1-4],andanotherworksinvestigatedtheexistenceofglobalattractorinR^nandΩ包含于R^n(n≤3)[5-6,11-12].Inthispaper,wediscussthedynamicalbehaviorwhenweapplyspectralmethodtofindnumericalapproximationforperiodicinitialvalueproblemofKGSequations.ItincludestheexistenceofapproximateattractorAN,theuppersemi-continuityonAwhichisaglobalattractorofinitialproblemandtheupperboundsofHausdorffandfractaldimensionsforAandAN,etc.
