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"unstable system" is a grammatically correct and usable phrase in written English.
You can use it to describe any kind of system or structure that is prone to sudden and unexpected change or dysfunction. For example, "Global markets have been increasingly vulnerable to an unstable system of economic policies."
Exact(60)
it would be an unstable system".
Competitive devaluation is an inherently unstable system.
"Like any unstable system, we may overshoot, we may bounce around horribly," warns Walker breezily.
He sees money as a liberating (though unstable) system of creating and exchanging credit.
Only a profoundly unstable system can be knocked over so easily.
The first is that capitalism is an inherently unstable system: like a Ponzi scheme, it has to keep growing.
One is that high income inequality creates an unstable system that is vulnerable to costly booms and busts.
However, we shouldn't be fooled into thinking that economic growth stemming from a fundamentally unstable system will generate long-term value for the UK.
Yet the causes of the 2001-02 crisis — jihadi terrorism, mutual suspicion, and a relatively young and unstable system of nuclear deterrence between the countries — have not disappeared.
A serious blemish on Giles MacDonogh's affable biography is his lack of interest in analysing William's position at the apex of a complicated and unstable system of power.
Earlier this year, that unstable system was thrown into further disarray by Louisiana's worst budget crisis in decades, which came in the wake of a steep drop in oil prices and years of tax-slashing by former governor Bobby Jindal.
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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