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The phrase "a protracted cycle of" is correct and usable in written English.
It can be used to describe a lengthy or drawn-out series of events or processes that repeat over time.
Example: "The community has been caught in a protracted cycle of poverty and unemployment for decades."
Alternatives: "an extended pattern of" or "a prolonged series of".
Exact(3)
Analysts expect that move to be the first step in a protracted cycle of rate increases.
Last week — after a protracted cycle of teasing, speculation, and delay — the John Dory Oyster Bar was almost ready to open.
What I believe is that everything is written in the stars--the story of our planet, our solar system, our own individual existences--all existed in blueprint form and go through a protracted cycle of birth, life and death.
Similar(57)
Then, this last year, after another protracted cycle of negotiations, the company mandated the implementation of another health insurance program that Peterson said was not worth enough for anyone in the company to use it.
The protracted cycles of commercial aircraft production require the unit's CEO, Alan Mulally, and his leadership team to take a long-term view of the business.
All tube-nosed birds have a protracted life cycle conditioned by their evolution and oceanic environment.
More debt may be undesirable, but a protracted deflationary cycle would be agonizing.
Planes have historically had a protracted production cycle; to design, assemble and certify a new aircraft takes considerable time.
The money is supposed to meet a "protracted balance-of-payments need".
Zolotova and Ponyavin (2014) reported that the protracted cycle 23 is similar to the cycles immediately preceding the Dalton and Gleissberg-Gnevyshev minima, suggesting that the Sun is heading toward such a grand minimum.
He now faces the prospect of a protracted criminal trial of his former comrades.
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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