  We consider a generic higher order mass aggregation term for interactions
between particles exhibiting oscillatory clumping and disaggregation behavior
in the F ring of Saturn, using a novel predator-prey model that relates the
mean mass aggregate (prey) and the square of the relative dispersion velocity
(predator) of the interacting particles. The resulting cyclic dynamic behavior
is demonstrated through time series plots, phase portraits and their
stroboscopic phase maps.
  Employing an eigenvalue stability analysis of the Jacobian of the system, we
find out that there are two distinct regimes depending on the exponent and the
amplitude of the higher order interactions of the nonlinear mass term. In
particular, the system exhibits a limit cycle oscillatory stable behavior for a
range of values of these parameters and a non-cyclic behavior for another
range, separated by a curve across which phase transitions would occur between
the two regimes. This shows that the observed clumping dynamics in Saturn's F
ring, corresponding to a limit cycle stability regime, can be systematically
maintained in presence of physical higher order mass aggregation terms in the
introduced model.
