My dogs, Sadie and Riley, chase one of my cats-Bevo (pronounced Bee-vo, named after UT's mascot because he's the darkest orange cat my ex-bf and I had ever seen). Thomas and Turbo, the other two cats, are the most dominant animals in my house, with Thomas being alpha, then comes Riley, Sadie, and poor Bevo. (For those of you that remember Thomas' cancer story, he's still hanging on and doing just fine. We've been very lucky.
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Thomas pretty much gets his way all the time. Here's a picture of him eating dog food with Sadie (out of Riley's giant bowl-Riley had claimed Sadie's bowl). He popped her shortly after the picture was taken... I guess for taking up too much space, so I had to take a handful of food out for him and move the bowl for Sadie. LOL Obviously, he has me trained, too. He often prefers to sleep in my bedroom on the bed with the dogs while I'm away, while the other two cats sleep on the couch or dining room chairs. He also likes to claim Riley's giant dog bed at night, and he likes to walk as slowly as he can down the hall when the dogs are behind him, b/c he knows they won't pass him. He will saunter down the hall, fluffing his tail, stopping to stretch, just so that they can't move any faster. He's a character.