Does anyone have information on this lawnmower

It's made by AYP, american yard products. They make mowers for MTD and others, even sears.

Where can I buy parts for a 1988 centarl park rideing mower

It's made by AYP. You need to know the model number to be able to look up the part number. That should be on a metal or foil plate maybe under the seat. The model number will be like CP12542 . That indicates Central park 12.5 HP 42 in cut. A 18 hp 38 cut would be CP18038. Go to http://www.m-and-d.com/parts.html use their part's diagram feature and get your part numbers. Then either buy from them, or do an eBay search for that number to see if someone has that particular part available. Another choice is a lawn mower boneyard to scavenge used parts.