The phrase "assert their dominance over" is correct and usable in written English.
It can be used in contexts discussing power dynamics, control, or authority in various situations, such as social, political, or competitive environments.
Example: "In the animal kingdom, males often assert their dominance over rivals to secure mating rights."
Alternatives: "establish their superiority over" or "exert control over".
The more apt comparison might be to 1995-96, when Republicans were riding high off the 1994 Republican Revolution and trying to assert their dominance over Clinton.
Why? Because, as we outline in a paper published this week, given the way in which an innovative economy works, there are manifold ways in which reapers of bad rewards can assert their dominance over the innovation process, and extract from it value that they did not create.
In a militarist society, guns are associated with vitality, sexuality, strength, one's ability to defend oneself, as much as to assert their dominance over another.
No matter how many smiles or pleasant assurances you give, there are some people who want to use a two-minute interaction in a shopping centre to assert their dominance over you.
This defeat began what some refer to as the "century of humiliation" in China, in which China's power and prestige faded as Westerner powers and Japan would assert their dominance over the Chinese population.
Thus "bull people" or "bull humans" are confused bulls, quite often feeling that they have to assert their dominance over humans and interact with humans, not others of their kind.
He said chancellors could use Budgets as a platform for asserting their dominance over domestic policy.
Until the eighth, the Braves were asserting their dominance over the team they had beaten in 19 of their last 25 regular-season meetings, and in the National League Championship Series last October.
Australia again asserted their dominance over New Zealand, South Africa and England, winning the series and comfortably beating England twice - in the process scoring 121 points against them.
Here, sexual violence against western women seem to be politicised rather than depoliticised by calling on politicians yet in a way that has the appearance of western men asserting their dominance over 'their' women.
To assert their dominance not only over a culture that had lived on the land for thousands of years before them, but an entire region of the world.
