It is not possible to keep the application scope in-sync
across a cluster.
To clarify, it is possible to replicate the session scope in
a cluster (via J2EE session replication), but the application scope
only exists in its own "sandbox" so to speak on each server.
Session scope aside, if you're looking to share data across a
CF cluster you should do so with a shared resource (e.g...a shared
file system or preferably, a database)