No. I think his behaviour will only get worse. This is because if you obey... You will have willingly given him the power to control you, and he will take advantage of that.
It's not lack of attention that makes a person abusive... It's insecurity already present in his nature. It was in this person's nature before they got into the relationship, and it will be there after the relationship ends. The insecure nature will no doubt show itself in every romantic relationship this person has, unless he gets professional help.
Control freaks are always insecure. At first the insecurity is because they haven't got whatever it is that they are seeking. Then once they have "it", the insecurity lies in their paranoia that they might lose "it". In the case of "it" being their lover. Their jealousy and abuse alienates their lover, and once they see they are pushing away that person, they become even more possessive in trying to hold on to what they are losing.
If you're with such a person... Leave, but don't do so in haste. Have a plan. Have a place to go. Also before you leave, let your place of employment know that you are leaving an abusive relationship, so they can let their security team know to keep him off the workplace property. Also once you leave, immediately seek a restraining order. A lot of abusive rejected lovers turn into stalkers.
If you have "no place to go"... See if there's a branch of Su Casa in your area. They are a non-profit organisation that deals exclusively with domestic violence victims of all sorts.