Albuquerque has a special free program that tries to control the population of stray cats. They will provide humane traps, you catch them and take them in, the cats are neutered, then they will return them to the area where they were caught. Simply eliminating the cats creates a "vacuum effect," which then allows a whole new population of stray cats to move in and claim the territory.
Cats that have been neutered through the Best Friends Animal Society have had the tip of the left ear clipped, making them a little easier to identify. Once as many cats as possible have been caught and neutered, they will provide suggestions to deter the cats from coming in your yard.
If you are seeing a lot of stray cats in Albuquerque and would like to help control the population, please contact this program. If you've been leaving cat food out for the strays, the program folks say please don't--it only encourages more strays to move into your area.
Apparently we have the "Kool-Aid" yard for cats--water, birds to watch or hunt, trees to climb and plantings to hide behind. Our area has a population of feral cats who don't belong to anyone and are not at all domesticated. Last year one of the cats had a litter of three kittens, so this year the population seems to have exploded, as other strays have also come into the area.
We aren't particular fans of cats. Besides being allergic to them, we find them leaving "gifts" in the flower beds, marking their territory, yowling and hunting my birds. The only upside is that we haven't had any mice at all this winter getting into my birdseed in the storage building.
Out of my research, everyone says the best deterrent is a dog. I'm good with that.