  The bifurcation period in low-mass X-ray binaries is the initial orbital pe-
riod which separates the formation of converging systems (which evolve with
decreasing orbital periods until the donor becomes degenerate) from the
diverging systems (which evolve with increasing orbital periods until the donor
star loses its envelope and a wide detached binary is formed). We calculate
systematically the bifurcation periods of binary systems with a 1.4M_\sun
neutron star and a 0.5-2M_\sun donor star, taking into account different kinds
of magnetic braking and mass loss mechanisms. Our results show that the
saturated magnetic braking can considerably decrease the values of bifurcation
period compared to the traditional magnetic braking, while the influence of
mass loss mechanisms on bifurcation periods is quite weak. We also develop a
semi-analytical method to compute the bifurcation period, the result of which
agrees well with the numerical method in the leading order.
