No, you dont have cycle. In the taoist tradition this is called to cut the red dragon and it has always been considered something good, not only because you then dont need anticontraceptives and can do a lot of tantric practices no problem, but above all because the taoist theory claims that the cycle involves a loss of chi, like ejaculation for men.
According to the theory, you anyway dont atrophize the system, so the moment you want your cycle again you can have it.
Taoist women used to cut the red dragon in many ways, not eating is a very fast one.
This is of course what happened in the past, but I wouldnt be too surprised if soon some breatharian girl came up being even pregnant. Its all very open always.