If the male is doing this then he may be telling her that he is the boss. Put the male in a room with food, water, cat toys, scratching post and a place to sleep. When you want the male out, put the female in the room and let the male out. Try not to let them come into contact with each other. I hope this works out for you!

Buy new litter boxes, possibly two. And let Felix have a room for himself. Don't allow Annie to go there. Keep Felix in that room and play with him until he is dead tired. Only then let him out to rediscover your home. Once he attacks Annie, put him in his crate until he calms down (if you don't have a crate use the room.)

When you let him out and he attacks again, put him back in until he's calm. Let Annie have the chance of sniffing him in his crate only if she dares--don't force her to do so. After all, it was her house before his, am I right? I am picturing Annie as a kitten and Felix as a cat because I'm not sure of their age. Annie should feel at home, and Felix should learn to behave. If necessary, spray him with a water bottle whenever he tries to attack her.

When he walks without hurting her, give him treats and use either a clicker or a praise word so he recognizes it just happens when he displays the certain behaviour (walk by the other cat, do nothing, get parent's attention and have a delicious treat) Show him that whenever he attacks, fun stuff stops. The free house space is gone, and treats are taken away. He gets locked up as soon as fighting starts, of course with water and scratching posts and the like, but gets ignored by humans until he's calm.

When he calms down, play with him and use the time to rub a towel (recently rubbed on Annie) all around his body. If possible, also play with him with it. Show him love and attention on a regular basis--he just doesn't get out of the room until he's calm. He should get the idea and behave more after a while. Thank you.

tl;dr– You can make safe spaces and defensive locations for your kitties. These can provide safety for the kitties as they try to eat or sleep, plus they can help deter bullying by making it a more difficult, less effective social strategy.

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Make safe spaces for the littler kitty.

I'd try making safe spaces for the littler kitty. It wouldn't be a full solution, but at least she could sleep and eat without fear of being attacked.

The easy solution would seem to be getting large, clear plastic storage bins. Cut at least 2 doors into each, where the doors aren't large enough for the bigger kitty to get in. Then you can put different items in them: a food bowl, a water bowl, a bed, etc.. Ideally, your little kitty could then retreat to these at any time, eating/drinking/resting in peace without fear of attack.

Abrasive-cutting tools (like a Dremel) seem to work well for cutting holes in plastic storage bins, but there're other ways to do it too. I sometimes line the cut edges to help smoothen them out. A lighter might be able to melt the edges to be smoother, too, but haven't explored that possibility yet.

If your littlest kitty grows, you may need to cut the doors slightly larger. If the littlest kitty gets to be about the same size, then these small-kitties-only zones may not work.

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Make defensive locations for kitties.

Some cats seem to like high, small perches where they can just barely fit. These are great defensive locations: a kitty can sleep there with relative comfort.

The trick's in it being hard for another kitty to get to the same location once it's already occupied. For example, if the location's accessed by jumping, but there's not a firm place for a second kitty to land, then it'd be hard for a second kitty to get a decisive win on the current occupant.

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Discussion: Creating an environment that reinforces positive behavior.

An open environment where the largest kitty can attack any other might allow for bullying/controlling behavior.

An environment where kitties have safe places and single-occupancy hideouts makes it harder for kitties to bully each other. While they might still try to do so in public spaces, the effectiveness of their bullying is limited when other kitties always have a safe way out, especially when the bully can't prevent others from resting/eating in peace.