  We present a time-dependent model of the interaction between a neutron star
magnetosphere and a thin (Shakura-Sunyaev) accretion disc, where the extent of
the magnetosphere is determined by balancing outward diffusion and inward
advection of the stellar magnetic field at the inner edge of the disc. The
nature of the equilibria available to the system is governed by the magnetic
Prandtl number Pm and the ratio \xi of the corotation radius to the Alfven
radius. For \xi > Pm^0.3, the system can occupy one of two stable states, where
the torques are of opposite signs. If the star is spinning up initially, in the
absence of extraneous perturbations, \xi decreases until the spin-up
equilibrium vanishes, the star subsequently spins down, and the torque
asymptotes to zero. Vortex-in-cell simulations of the Kelvin-Helmholtz
instability suggest that the transport speed across the mixing layer between
the disc and magnetosphere is less than the shear speed when the layer is thin,
unlike in previous models.
