It is also frequently overlooked that both the European (Roman) and Chinese situations vis-a-vis the 'Barbarians' included a lot of non-combat interactions - in the long run, probably a lot more.
The Romans traded with central Europe, Scandinavia and Germany from at least the first century on - they even had posts in central Germany guarding the trade routes and river crossings that brought amber down from the Baltic, for one example. German settlements across the Rhine from Roman settlements traded so extensively that there was a progressive 'Romanization' of them - most noticeably at modern Wiesbaden, occupied by the Matti tribe of Germans and right across the river from the huge Roman Legionary Fortress of (modern) Mainz: by the time of the Emperor Domitian, the settlement of the Matti was incorporated as a Roman City (the original Roman city gate is still in modern Wiesbaden).
In China, it is often not appreciated that the Long (Great) Wall was built as much to keep Chinese peasants from absconding to the steppe as it was to keep 'barbarians' out of China. The fact that several crossing points in the wall were maintained to keep trade flowing - and controlled for taxation purposes - also indicates how important non-combative trade and contact with the 'Northern Barbarians' was to the Chinese Dynasties. This extended to trade in people as well: DNA studies are starting to show surprising amounts of non-Han elements in parts of the Chinese population, dating back to at least the Tang Dynasty, which included a surprising percentage of 'Barbarian' DNA in their aristocracy!
This, of course, is also paralleled in Europe: the plagues of the 3rd century so depopulated parts the western Roman Empire that Germanic groups were allowed or invited in long before the 'invasions' of the 5th century, and the 'Germanicization' of the Roman Army was a feature of the last 2 centuries of the Empire, up to and including the senior leadership of the Roman forces.
In this case, any Crisis related to interactions between the settled states and the 'barbarians' took place at both ends of the Eurasian continent.