Ex girlfriend problems help anyone please?

ok me and my ex have been together for three years we broke up in september so its been like three months. she started dating someone else in october which doenst bother me im a very confident guy so it was like what ever to me.since we broke up though she has been having these mood swings with me one second shes like she wants me in her life and she wants to be with me again then the next day she will be like i want to be with him. our relationship wasnt too good at the end thats why we broke up. But she is gong back and forth with me and we have been having still even though she is in this relationship with this other guy.she tells me she really likes him and possibly loves him and that she doesnt want to be with me then two days later shes at my house saying she loves me and wants me and its just a ridiculous cylce of this. But last week she was like she doesnt feel the same anymore that something feels different between us and she thinks she wants to be with him then we had right after like wtf. then the next day i said goodmorning babe and she asked me to not call her that and treat her like she has a boyfriend. i said ok. That night we were on skype and basically we are back to square 1 we are going bowling tonight and probably will have some time soon i dnt understand her. i told her numerous times i will not be her friend so dnt expect me to act like one she says she understands and yet she still wants to hang with me knowing shes probably gonna end up cheating on this new guy with me. i love her i do i cant lie i want her but im so confused. she tells me one second she wants him and what not then shes at my house cheating on him what should i do, Any advice would help but can you say more than just leave her like i could think of tht by myself anyways thnx