"in periods" is a correct and usable phrase in written English.
It can mean: -At regular intervals of time: We take breaks from studying in periods. -In several distinct sections of time: Our company is divided into periods of growth and decline. -During certain spans of time: The Industrial Revolution happened in periods of technological advancement.
Exact(55)
In periods of growth, companies hire aggressively.
Despite the score, the game was slightly dull in periods.
The situation gets worse in periods of drought.
We have to be united in periods of crisis".
("Quotations are useful in periods of ignorance or obscurantist beliefs").
In periods of full employment the situation is substantially different.
One-third are foreign species, introduced in periods of colonization.
In periods of recession, they can budget for growth.
Other trials of UBS bankers ended in periods of house arrest and probation.
Similar(2)
But ask about lock-in periods – you will normally be tied into an 18-month contract.
Physicians use run-in periods every day in real life, and trialists have used run-in periods for decades to reliably establish the role of new cardiovascular drugs.
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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