We implement a dynamical model that describes the polarization
behavior in VCSELs containing an absorbing region surrounding the
active zone. We find four regions of qualitative different
behaviors: stable linearly-polarized operation, intensity
pulsations of a linearly-polarized component, pulsations of both
total intensity and polarization components, and polarization
self-pulsations with constant total intensity. We characterize the
four regions by computing the polarization resolved optical and
power spectra. The predicted scenario agrees with recent
experimental results.