Imagine an $N$-body problem with lots of particles of identical mass (billions of them).
I saw several simulations on the Internet, where the particles first form small clumps, then bigger clumps, then finally one huge globular cluster like clump around the center of mass.
Is this clump a stable feature? If we keep running the simulation forever, will this cluster stabilize and remain there forever, or will the particles gradually leak away so that the cluster dissolves?
Clarifications:
The particles attract each other gravitationally (so if the distance is $r$ between two particles, the attractive force between them is proportional $1/r^2$).
Initial conditions are unconstrained, and indeed if the particles are too fast then it can't be bound gravitationally. So probably it's a function of kinetic energy and gravitational potential energy in system, but what function?
If you want me to mention a particular situation, then consider a globular cluster, for example.
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