Luki thinks very much like a territorial dog. He wants love, and he'll do anything for the people who give it to him. But once that love is threatened, in any way, he starts to panic and turns violent. But it's a protective violence; he's doing it to protect himself from heart break. And because of the errors in his programming, to him, that's a perfectly good reason to be violent.
This, to me, correlates with the song. At first, the singer is just happy to be around the person they love even if that person doesn't actually know or love them. This is very much like a dog; as long as you aren't abusing them, and the dog doesn't know anything other type of love, a dog will love you with their whole heart and soul even if you only barely give them attention. And they'll love you forever.
But if you suddenly introduce another dog to the environment, (like how the singer sees the person they love with someone new) whom you give more attention and love too than the first dog gets very jealous. And should the first dog continue to be neglected it will begin to hate the new dog.
I'm not entirely sure if the metaphorical dog would come to the same conclusion as the singer of Love Disease did, which is to kill the new dog, but if they did and they're owner was suddenly afraid of them it would correlate once again.
The singer is confused at this point; why won't you talk to me? Why won't you give me the attention you were giving that other person? I love you! Why don't you love me?
To them the problem should be fixed- they don't want to hurt you, they want to love you. So why are you afraid? The final act of desperation(the singer killing the one they love) is less dog like, but very yandere. You ran. They snapped. It's the only way they they can keep you.
Now this situation from the song has been avoided in the dressing room- he got the love he wanted. However, finding out that his love's heart was not entirely his, has triggered the territorial behavior and jealousy. He's panicking and struggling with how to deal with it. But I'm sure this can be fixed! Or, I hope so.
TLDR; Luki is a territorial puppy thinking 'love only me, look at only me, I'll never leave you! Just stay!'
Len is far more messed up than Luki. Wether it was something wrong with his programming, or just his life experiences, Len has become covetous of everyone and anyone with a happier life than himself. Why should they be happier than him? Why should he be the one with an irresponsible master that ignores him?
And that jealousy turned to rage, which led him to hurting(killing) others of his own kind. It makes him feel better. But, because he knows it's wrong, he struggles to justify his actions and pacify the guilt piling up. The guilt, in turn, has made him somewhat unconsciously attempt to punish himself by pushing the person closest to him(Rin) away. He feels he doesn't deserve her, and that his being around her has ruined her. Their now tense relationship has only furthered these beliefs. But because he still wants happiness, and he still wants her, his behavior towards her has become as erratic as his turbulent mind.
TLDR; Self-destructive yan wants dere.
Rin, by no stretch of the imagination, cannot be solely classified as just a yandere. She's had something wrong with her head since birth. She's insane. She's pure evil. She hurts everything she touches, and she doesn't care. The only person she even has the 'dere' side for is her brother, and even so she began breaking him long ago. But the dere she does have for him is deep, twisted, and dangerous. Anyone who gets too close to her Len is automatically on her list.
TLDR; Girl is crazy.
And so concludes the random character study of my three yandere vocaloid muses.
TLDR; I LOVE YANDERES AND PUT TOO MUCH WORK INTO THEM. xD