Gonzo will freeze in place, and stare down said cat... for hours on end. If cat moves, he will slowly follow, and procede to stare. If said cat attempts to initiate contact, he will tuck his tail pathetically, move a few feet away, and carry on with the staring.
Fozzie will find a way to convince the cat to play. Even cats that despise dogs, for some reason, will end up playing with him. ;3