  We discuss the {\it SU}(2) chiral sigma model in the context of nuclear
matter using a mean field approach at high density. In this model we include a
dynamically generated isoscalar vector field and higher-order terms in the
scalar field. With the inclusion of these, we reproduce the empirical values of
the nuclear matter saturation density, binding energy, and nuclear
incompressibility. The value of the incompressibility is chosen according to
recently obtained heavy-ion collision data. We then apply the same dynamical
model to neutron-rich matter in beta equilibrium, related to neutron star
structure. The maximum mass and corresponding radius of stable non-rotating
neutron stars are found to be in the observational limit.
