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"fluctuate over" is a correct and usable phrase in written English.
It is used to describe how a value changes in relation to a defined period of time. For example, "The average cost of rent in this area has fluctuated over the past decade."
Exact(59)
Moreover, the persistence of implemented changes may fluctuate over time.
Presumably underlying genetic variation takes some time to develop and may fluctuate over time.
Utility values may fluctuate over time as individuals adapt to a given health state.
One loss can trigger other losses so that there is a cascade of adverse events, and felt adversity might fluctuate over time.
"What I do know is that wildlife populations fluctuate over time for a number of reasons.
Incomes fluctuate over a lifetime for a variety of reasons – and much more than we tend to assume.
Asylum numbers do fluctuate over time depending on the state of the world, and Europe has witnessed significant spikes in numbers before.
The transform can also be applied to clean up pictures which are, in essence, just two-dimensional signals where colour and brightness fluctuate over space.
The depths of these deep and shallow water tables in hills fluctuate over time.
The shares will fluctuate over the course of an interest rate cycle.
However, several factors influence the model that fluctuate over time, and on different timescales.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com