i have 2 dogs and 2 cats and i find my gsd dog is obsessed with my cats....he is actually stalking them
They have all upstair the cats and he sits downstair guarding the stairs incase they want to go to toilet lol
Or when they with us on their tree he sits and watches them until he falls asleep.
And when they try to walk out the room he runs after them....but i find if u have the leave command trained well that helps a bit. as mine makes a abrupt stopp when i shout leave lol but sometimes i just have to grab hold of him as he gets so excited.
Also u should never allow the dog chasing them and try to stop it however u can as this will develope into a fun game for the dog and it will be harder to stop.