Syncrhonized database

I have to develop a desktop application for management school system. It must be used (offline) by several people on different computers connected to the local network. how to design the database so that the applications installed in each computer exchange data. knowing that the applications are fully operational even when they are not connected to a network. And can be updated during connection if there have been changes made by another computer on the network. Which architecture to use for the database? and which databases to use for this case? Thank you for your response ...