[burnished]

The part you aren't mentioning is that in your model cat populations decrease when they cant find enough birds, which allows for the birds to repopulate, which allows for the cats to catch them and repopulate.

The feedback cycle is broken where the cats have ample food supplied and the cat population no longer depends on the prey population.

[bradknowles]

There are plenty of outdoor or indoor/outdoor cats that kill for reasons other than food. Some cats just have a strong sense of prey.

[burnished]

Yes, thats integral to the point I'm making. Cat populations aren't being modulated by prey specie availability but they are still killing. A healthy ecosystem maintains a balance between predator and prey because their population numbers depend on each other. But cat populations that are being maintained by humans don't have that feature, hence the outsized impact of their predation.