My mats came with a plastic gizmo that hooks to the carpet like Velcro and holds the mat in place...
If you can't find these on amazon.com you may want to try a roll of that area rug pad stuff with removable stickiness on one side and grippy rubber surface on the other side. You could affix a strip or two of it to the bottom of your new floor mat and see if it keeps it in place.
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