Three year old is extremely jealous of our one-year-old, and it's not getting any better

Since our one year old was born, our three year old has always been extremely jealous of him. I completely understand that's normal. After being the center of attention for the first two years of his life, then suddenly the attention is being shared. I get it. We have done our best to give him as much attention as he wants, but I don't feel like it's getting any better.This week has been particularly bad. Last week was the one year old's birthday, so we bought this push car thingy: https://ift.tt/30IHxgR really annoyed our three year old extremely badly and since then he's been worse than ever.He's being extremely aggressive towards our one year old. He pushes the one year old, head butts him, or growls at him. He even takes the car, and plays with himself, and won't let the one year old even touch it. If he sees him playing with it, he will push him off. We've tried explaining it to him that he has to share, and even explained that it's not his toy. In-fact, last month when it was his birthday, we bought him a bicycle as well. I get he's only three, and he isn't very good at sharing, but I really don't know how to proceed at the moment as his aggression has only increased regardless of what we do.When they wake up in the morning, our one year old usually walks to our three year old's bed with a huge smile and wants to play with his big brother, but then we hear "NO. I DON'T WANT YOU!" a long with our one year old crying because he just got hit.Normally we put him in time out when he does something like this, but honestly it feels like it's just getting worse, especially this week his behaviour in general has been extremely bad.I feel like he just doesn't care when he does something bad. Like he wants to trigger a reaction from us.This week has been so extremely tough because of him. The non-stop crying, bullying our one year old or general bad behaviour (eg he throws his cars down the stairs, or intentionally spills his water while making eye contact, and refusing to clean it up).I would greatly appreciate any advice you could give me at how to handle this, as both me and my wife are totally lost at how to calm his jealousy. via /r/Parenting https://ift.tt/2OTHGZh