We considered a high birefringence fiber ring cavity, which can be represen
ted by a system of two incoherently coupled nonlinear Schrodinger equations
with periodic boundary conditions. The stability of the system against tim
e domain periodic perturbations could be strongly conditioned by fiber bire
fringence. We apply both a perturbative approach and a mean field approxima
tion, in order to highlight the dependence of modulation instability on bir
efringence and ring detuning. We extend the study of the dynamical properti
es of the system by means of a phase matching interpretation and a selectio
n of numerical solutions of the governing equations.