Optical and X-ray spectroscopy indicate that the X-ray pulsar GX 1+4 is see
n through a cloud of gravitationally bound matter. We discuss an unstable n
egative feedback mechanism (originally proposed by Kotani et al. 1999), bas
ed on X-ray heating of this matter which controls the accretion rate when t
he source is in a low X-ray luminosity state. A deep minimum lasting simila
r to 6 hours occurred during observations with the RXTE satellite over 1996
July 19-21. The shape of the X-ray pulses changed remarkably from before t
o after the minimum. These changes may be related to the transition from ne
utron star spin-down to spin-up which occurred at about the same time. Smoo
thed particle hydrodynamic simulations of the effect of adding matter with
opposite angular momentum to an existing disk, show that it is possible for
a number of concentric rings with alternating senses of rotation to co-exi
st in a disk. This could provide an explanation for the steplike changes in
(P) over dot which are observed in GX 1+4. Changes at the inner boundary o
f the disk occur at the same timescale as that imposed at the outer boundar
y. Reversals of material torque on the neutron star occur at a minimum in L
-x.