  Nonlinearities in constitutive equations of extended objects in shear flow
lead to novel phenomena, {\it e.g.} "rheochaos" in solutions of wormlike
micelles and "elastic turbulence" in polymer solutions. Since both phenomena
involve anisotropic objects, their contributions to the deviatoric stress are
likely to be similar. However, these two fields have evolved rather
independently and an attempt at connecting these fields is still lacking. We
show that a minimal model in which the anisotropic nature of the constituting
objects is taken into account by a nematic alignment tensor field reproduces
several statistical features found in rheochaos and elastic turbulence. We
numerically analyse the full non-linear hydrodynamic equations of a sheared
nematic fluid under shear stress and strain rate controlled situations,
incorporating spatial heterogeneity only in the gradient direction. For a
certain range of imposed stress and strain rates, this extended dynamical
system shows signatures of \textit{spatiotemporal chaos} and \textit{transient
shear banding}. In the chaotic regime the power spectra of the order parameter
stress, velocity fluctuations and the total injected power show power law
behavior and the total injected power shows a non-gaussian, skewed probability
distribution. These dynamical features bear resemblance to \textit{elastic
turbulence} phenomena observed in polymer solutions. The scaling behavior is
independent of the choice of shear rate/stress controlled method.
