it's nothing like the same as stopping it chasing livestock, you want it to catch rabbits etc. most of the time, you never want it to chase livestock so it shouldn't run after livestock no matter what.
No but it is kind of similar to the control needed to do the following - take one hungry dog, make him sit, place a bowl of really tasty meat in front of him and watch him sit there for 10-15 mins wanting the food so bad but not moving a muscle, before you give a command and only then does he eat. Not quite but close. It's also how you tell the dog to leave things it doesnt understand yet