Changing the $DISPLAY variable in ubuntu server xfce, what's the problem?

Question

ubuntu

Greetings to all, today there is a need to automate a certain process. Ubuntu server with xfce graphical shell was chosen. A script was written and set to autorun for every hour in cron. Cron, to launch GUI applications, it's easy to specify the display using the export DISPLAY= command: But the fact is that the $DISPLAY variable changes once a day in the remote desktop, usually from 10.0 to 11.0, and the script naturally stops working. On the command line, the $DISPLAY variable is always the same. Tell me what is the reason for this, and how can I fix it?
PS In ubuntu, a complete zero, in server administration, too.