  We present the results of a numerical study of a model of the hydrodynamics
of a sheared nematogenic fluid, taking into account the effects of order
parameter stresses on the velocity profile, but allowing spatial variations
only in the gradient direction. When parameter values are such that the stress
from orientational distortions is comparable to the bare viscous stress, the
system exhibits steady states with the characteristics of shear banding. In
addition, nonlinearity in the coupling of extensional flow to orientation leads
to the appearance of a new steady state in which the features of both
spatiotemporal chaos and shear banding are present.
