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The phrase "a long established cycle of" is correct and usable in written English.
You can use it to describe a repetitive pattern or process that has been in place for a significant amount of time.
Example: "The community has been caught in a long established cycle of poverty that seems difficult to break."
Alternatives: "a deeply rooted pattern of" or "a well-entrenched cycle of".
Exact(1)
Most don't deny that the world's temperatures are rising or that the climate is changing, but they argue that such changes are the continuation of a long established cycle of environmental readjustment and that anthropogenic causes are not powerful enough to produce such effects.
Similar(59)
The designer announced that he, too, is breaking high fashion's long established cycle of showing clothes on the catwalk six months before they are available to buy.
The company now has a long established tradition of performing musical and operetta alongside heavier repertoire.
Kato was a long established master of operator theory.
"Gabe is focused on sticking a rocket under Microsoft, while Richard is speaking from a long established point of view.
They describe a long established practice for the management of the stoma (cleaning and change).
This finding solves a long established paradox in LD.
"There's currently a long-established word-of-mouth system that will trump any ranking system," he says.
Fortunately the Chinese have a long-established habit of taking the long view.
But growth still relies heavily on a long-established recipe of infrastructure investment and building projects.
Burano has a long-established tradition of needle-lace making, though precise historical records are lacking.
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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