Some (most? all?) pets have a problem eating their food and only their food. The 'big dog' will eat his own food while driving the other away from his, then eat the other's food.

Business idea: pet bowls that have a RFID in them, and (weak) shock collars for your pet. Each bowl would transmit on a particular channel that you tune the bowl to. When the wrong animal sticks his head down to the bowl, he gets a mild shock. In a short while, only the pet who belongs to the bowl will eat from that bowl. Of course, the bowls should be differently shaped so the pets can tell them apart without being shocked.

Also useful if you need to put medication in the bowl of one pet but not another.