Without great power competition, the five great powers can afford to ignore the turbulence on the periphery. Bosnia is the exception that proves the rule. It was difficult to ignore entirely because it is situated on the border between the core and the periphery. It both is and is not in Europe. Despite all that has happened in Bosnia, however, there is clearly a limit to what the great powers are willing to do there.
Peacekeeping seems to be all that Western publics are willing to support.
A second source of instability is rarer but more important, and could be the occasion for great power intervention. Nuclear proliferation as a source of instability on the periphery is important to the five major powers because it has the potential to alter regional balances and affect vital interests. The core, led by the United States, intervened in the Persian Gulf among other reasons to thwart the Iraqi nuclear weapons program and may yet do so for the same purpose on the Korean peninsula. Among the major powers, the role of the United States is to do what is necessary to preserve stability, which is to maintain a military presence of some kind in Europe and the Asia-Pacific region. The task of the United States, given the post-Cold War configuration of power and politics in Europe and East Asia, is to reassure the major and lesser powers of both regions that there will be no abrupt change in geopolitical conditions.