So, I think one of the key features of an Empire is that those who rule it are perpetually in fear of losing it. It's one of the key tenets of imperial psychology that has been seen, at least throughout the modern era (I don't know much about the ancient, but from my limited understanding it seemed that Rome at least was very aware of losing its control over conquered lands and tributaries.) There are some interesting theories we could come up with as to why this mindset is so prevalent, but to start I'll try and lay out some examples I have.

I'll take it just case-by-case here, not massively comparative as I don't have loads of time sadly, and these are just brief summaries, but hopefully you can begin to see some of the themes emerge.

Firstly, Britain. One of the key elements noted in George Orwell's semi-autobiographical Burmese Days was that his fellow colonial officers in India in the 1920s was that they were terrified of the "natives" rising up and overthrowing the British. It was dominant in conversation, strategy, relationships, and the overall construction of British identity in India. This has also been demonstrated through the collection of personal stories in The British In India, but some of the better analysis that I've read on this has been by Kim Wagner about the 1919 Amritsar massacre. They highlight the similarities between the British response in this event and the earlier 1857 Indian uprising - essentially, the British continually feared fierce violence from their colonial subjects, and consequently used brutal force in order to hopefully "suppress" the subjects. Similarities here can also be seen in the 1950s 'Mau Mau' uprising in Kenya, or even in the 1800s wars in South Africa, whether against Africans or Afrikaaners. Essentially, Empire is inherently violent, and violence leads to hate and the fear of the conquered retaliating against the conquerors, leading to further violence. A fun cycle. It's also partly why Britain always made such efforts to have local leaders onside - whilst 'divide and conquer' is a simplification, the principle of it was certainly valued highly.

Moving next to look at Spain in the 19th and 20th centuries, a similar sense of fear could be seen. Spain is a really interesting imperial example to look at thanks to how it experienced decolonisation earlier than the other major European powers. The loss of its colonies caused such an identity crisis in Spanish politics that the idea of the "Black Legend" developed (though this was largely actually driven by other European power's portrayals of Spain), essentially a desire in Spain to try and establish why it was that they were crumbling whilst other European powers were still ascendant. Consequently, when their Moroccan colony was threatened by local uprisings in the 1900s, Spain reacted with brutality driven by fear of losing their last claims to Empire. One of the reason Franco experienced early success in the 1930s Civil War was because the core of his army was formed of the experienced soldiers (both Spanish and Moroccan) who had brutally suppressed rebellions. Spain was keenly aware of its loss as it happened, and this reinforced the desperation to maintain its colonies as its empire finally crumbled away piece by piece. There is a lot more on this to explore, as it was a lengthier process than I've laid out here, but hopefully the idea is clear.

Next, we can consider the U.S. Few historians today, that I am aware of, continue to argue that America was not an Empire. It conquered the size of a small continent, colonising the land. Furthermore, it then gained overseas colonies (Hawaii, the Philippines) and exerted huge influence over other states, to the point of them in many ways becoming tributary states. Dominant throughout U.S. history has been its idea of "Manifest Destiny," claiming its place in the world. Underpinning this belief has been the flipside - the fear of losing what they believed was theirs. This could most clearly be seen in racial tensions, thanks to how heavily America was dependent on racial slavery and racial divisions in its foundation and expansion. The American Indians were portrayed as savage, to be eternally feared, coralled, and at many points even debated about pushing to 'extinction.' This violence was built upon the fear that the American Indians would try to reclaim their land. And, of course, these racial tensions were deeply present regarding the enslaved Africans who found themselves in American society. We still see today how America struggles to determine whether it views Black Americans as Americans or as an enemy that could bring the Empire down - this was really highlighted back in the 1960s (look at the theories of the Black Panthers, for example, and Malcolm X, about Black Americans as colonial subjects). You can also see this fear of losing global power in regards to earlier events such as the Vietnam War, and more recently Afghanistan.

Finally, if we look briefly at Russia. It's important to remember that Russia was a multi-ethnic, multi-national empire including thousands of cultures and peoples. During the Russian Civil War of 1917-23, one of the key fears of the 'Whites' (or more specifically, the ex-Tsarist, Tsarist, and generally conservative elements of the Whites) was the breakup of the Empire. They were furious at the idea of greater autonomy, let alone independence, that many of the Empire's nations were claiming, most notably Finland, Poland, and Ukraine. The weakening of the Empire was one of the key reasons that many who went on to join the Whites were actually okay, to some extent, with removing the Tsar - they felt that, above all else, the integrity of the Empire had to be maintained. If you read some of the autobiographies of conservative Russian exiles, such as Denekin, Got'e, or even the "socialist" Kerensky (widely accepted to not 'really' be a Socialist from what I've read) the sense of despair felt over the collapse of the Empire is evident and clearly keenly felt.

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Okay, I know that's a lot of fairly random examples chucked together, I'm sorry I don't have the time to really tie them together much or add some commentary on the Chinese Empire (well worth investigating!) or medieval/ancient Empires, but, from what I've researched, Empire's cause deep fear in the rulers as they are desperately aware of what they have conquered and that those under them tend to want to get out. The imperial power continually believes itself to be on the brink of collapse, needing fierce vigilance over its subjects. It utilised every tactic available, including but not limited to violence, to maintain its power. Any hint of difficulty brings its nerves to the surface, in turn then reinforcing its neurotic fear and increasing the cycle. Eventually, when final collapse comes, it's often spoken of in very similar terms of the non-consequential events as before (so with great alarm), only now it turns out the fears are founded.

I'm out of time so won't list sources here, especially because what I've read on these is pretty wide but also buried in notes etc. and I don't think a random huge list would be too helpful haha. Hope this helps!