  We study the role of the control parameter triggering nematic order
(temperature or concentration) on the dynamical behavior of a system of
nanorods under shear. Our study is based on a set of mesoscopic equations of
motion for the components of the tensorial orientational order parameter. We
investigating these equations via a systematic bifurcation analysis based on a
numerical continuation technique, focusing on spatially homogeneous states.
Exploring a wide range of parameters we find, unexpectedly, that states with
oscillatory motion can exist even under conditions where the equilibrium system
is isotropic. These oscillatory states are characterized by wagging motion of
the paranematic director, and they occur if the tumbling parameter is
sufficiently small. We also present full non-equilibrium phase diagrams, in the
plane spanned by the concentration and the shear rate.
