Have a 3 yr old Yorkshire Terrier who is starting to nip at the ankles and is very jealous since getting a cat.
Hi Your dog is 'acting out' because he feels jealous and this is the only way he can think of to get your attention.
I'd recommend reading my Puppy Biting page as it has tons of tips and advice on dealing with this behavior. Although your dog is older, he's still using biting and nipping as an attention seeking behavior, and the same puppy biting correction methods apply.
Also, do try to give him a bit extra love and attention, but initiate that when he's being well behaved, not when he's biting or being a 'brat'. It's very normal for a dog to have issues when a new puppy (or cat) is brought into 'his' family, but with time, patience and love you'll be able to help him get over his hurt feelings. Hopefully he will soon see the cat as his friend (or at least not as his enemy!).