She would not stoop to admit that she meant to rival Gilbert in schoolwork, because that would have been to acknowledge his existence which Anne persistently ignored; but the rivalry was there and honors fluctuated between them.
There are no more uses of "fluctuate" in the book.
Show samples from other sources
Cattle markets tend to fluctuate a lot, and some years, you don’t make much of anything.
Nicholas Sparks -- The Longest Ride
My courage and my resolution is firm; but my hopes fluctuate, and my spirits are often depressed.