Ayu hasnt invented a new style of music, she just made the vibrato a part of her style, if you hear her vibrato you can know that it's she even if you dont recognize the song.
I always sing her songs and i try to imitate almost all notes, but well it's hard when you are a boy and you havent got a very sweet voice, but the point is that when i sing them with vibrato i really feel that i'm singing them right.
Just like to sing an ayu song without vibrato is to sing a normal song, not an ayu song. By the way I ask myself when and why she became the vibrato her natural sign.