Origin of cusps in simulated dark matter halos I keep reading that cusps are one of the most "robust" predictions of N-body simulations of dark matter halos. But papers I've found on the topic make it sound like these simulations are complicated and slow and that the cusps are just an observed result of the simulations rather than that the cusps have some understandable physical origin. But my immediate reaction was that the cusps' origin is trivial (just the result of phase-space considerations) and that interaction-less dark matter simulations should be one of the easiest things in the world. 
I remember writing a program to simulate non-interacting particles orbiting each-other with an inverse square law on an old PC over a decade ago, and I recall being able to get a pretty good picture of the density profile by tracing the paths of just a few particles. This only took a minute or two on a very slow PC. Indeed I remember something of a cusp being obvious, simply because the orbits of each particle tended to intersect near the CM, an effect that overrode the countervailing fact that individually each spent less time near the CM. 
In fact, even without doing a simulation, I would assume this would be the case because Keplerian motion clearly indicates that the time spent near the CM drops close to linear in R while volume goes as R^3. Anyway, I'm just wondering if these observations are basically correct, or if the origin of the cusps is somehow more obscure/complicated.
 A: Wikipedia has this entry about the cuspy halo problem

"The cuspy halo problem arises from cosmological simulations that seem to indicate cold dark matter (CDM) would form cuspy distributions — that is, increasing sharply to a high value at a central point — in the most dense areas of the universe. This would imply that the center of the Milky Way, for example, should exhibit a higher dark-matter density than other areas. However, it seems rather that the centers of these galaxies likely have no cusp in the dark-matter distribution at all.
  "

I think the last sentence could be interpreted thus "... it seems from  actual astronomical observations and interpretations/models based on observations that... there should not be a cusp in DM density at the centre of a galaxy".
Thus it seems to me that your simulation (for whatever reason) agrees with more sophisticated simulations in predicting a cusp whereas actual astronomical observations suggest that there should not be a cusp.
A: Cusps are an obvious consequence of the usual DM models to me too. 
It seems that there are so many problems with dark matter theory that something is obviously wrong.
We have the cusp problem, the lack of DM in the nearby region of of our galaxy, the failure to find any in experiments, and more.
By far the biggest problem with DM though is the complete lack of its prediction, given that we have so many smart theoreticians! Ditto of course on the dark energy front.
I really like how observational astronomy is working on the third decimal place of DM abundance. To physics however there is not even an acknowledgment of any problem.
I thought I was commenting ...
To turn this into an answer,
There is no need for complicated models to model the cusps, they come about when making models for the entire matter -DM structure.
