  This paper explores the dynamics of evolving cluster of stars in the
presences of exotic matter. The $f(R)$ theory is used to presume exotic terms
for evolution scenario. We use structure scalars as evolution parameters to
explore dynamics of spherically symmetric distribution of evolving cluster of
stars. We consider Starobinsky model, $f(R)=R+\epsilon R^2$ and study different
evolution modes having features like isotropic pressure, density homogeneity,
homologous and geodesic behavior. It is concluded that dynamics of these modes
of evolution depends upon the behavior of dark matter. The presences of dark
matter directly affects the features of cluster like anisotropic pressure,
dissipation, expansion, shear as well as density homogeneity. The evolution
having homogeneous density and isotropic pressure depends upon conformally flat
and non-dissipative behavior of baryonic as well as non baryonic matter. The
dissipation factor induces density inhomogeneity in the expanding clusters
having shear effects. The non dissipative homologous evolution also be
discussed in the presence and absence of shear effects. It is found that high
curvature geometry in the presence of shear supports homologous evolution.
Expanding clusters are also explored in the presences of dissipation of dark
matter and shear effects. By using quasi-homologous conditions the geodesic
evolution is studied. It is theoretically showed that geodesic and homologous
conditions depends upon each other. Finally we investigate behavior of
Starobinsky model for a stellar structure $4U 1820-30$ toward center. It is
found that for increasing values of $\epsilon$ the DM behavior is dominant as
compare to baryonic matter.
