Cat-Mate 363 Electronic Pet Door
These are operated by one 9 volt battery (not included) so they don't require a location near a wall outlet. The doors sense the collar key, which is a small, waterproof magnet, and unlocks. The cat then pushes through. The pet doors are 'self-framing'. Two collar keys are included with each pet door.
The 08AM363 includes collar keys suitable for both a cat and a dog. Both key types will unlock both doors.
The 08AM363 doors use sliding tabs to accomplish the 4-way lock rather than a rotary dial (there are two red tabs and one green in the center).
You might suppose that one way to use the Cat Mate pet doors to keep one pet in while allowing another out would be to reverse the pet door so that it controlled pets on the inside but not, obviously then, on the outside. That idea works provided that you carefully shield the now outside portion of the pet door from the weather.
Note: Reversed installation (turning the pet door around so that it controls from the inside rather than from the outside) will void the warranty.
Another idea that we have encountered is installing two pet doors--one at each end of a fabricated wooden tunnel made long enough that the flaps don't interfere with each other. Then the outside unit controls access from the outside and the inside unit controls access from the inside. Such an installation would be easiest to accomplish in a wall.
Important note: There is a third slide lock mounted in the bottom center of the pet door which locks the solenoid*. However, several customers have misinterpreted its function, left the solenoid locked and thought that the pet door was malfunctioning. This is actually a handy feature to use in training.
*The solenoid is the colored (green and yellow) portion inside the base of the pet door that controls the electronic motion of the flap.