Our cats begin to run around chasing each other at 10 PM EVERY NIGHT!! Then, they calm down around 11ish and sleep until 5:00 when the alarm goes off.

It may help that we have two cats, they keep each other company during their bursts of energy. We also used to play with them right before bed or in bed with the laser pointer. They would get really sleepy and rest the entire night!

Good luck!