Cats typically begin to recognize their family members around two months after arriving home. However, from a cat's perspective, the owner is more like a friend or a mother figure, a trusted provider of food. Once a cat recognizes its owner, it will show affection and trust, always wanting to be close and purring contentedly. Furthermore, the cat will actively rub against people, showing affection and asserting ownership. Although cats are not particularly obedient, once they recognize their owner, they will turn around or run towards them when called. It takes time for a cat to recognize its owner, and owners need to be patient. As long as you give your cat enough love, they will definitely sense it. 
How a cat recognizes its family:
1. When the owner is sleeping, the cat always likes to stick close to the owner and will make purring sounds, which sounds very relaxed and happy. This indicates that the cat has recognized the owner.
2. Cats will rub against their owners' legs and meow affectionately. Cats are very possessive and will leave their scent on their owners by rubbing against them. This shows that they trust their owners and feel that their owners belong to them, and they want to use their scent to mark ownership.
3. Although cats are relatively unobedient animals, once a cat has recognized its owner, it will come immediately or turn around to look at its owner when the owner calls its name.
4. In addition, when cats have needs such as eating or drinking, they will come to find their owners immediately.