  Motivated by the observation of rheochaos in sheared wormlike micelles
[Bandyopadhyay et al., Phys. Rev. Lett, 84 2022, (2000); Europhys. Lett. 56,
447 (2001); Pramana 53, 223 (1999)] we study the coupled nonlinear partial
differential equations for the hydrodynamic velocity and order parameter fields
in a sheared nematogenic fluid. In a suitable parameter range, we find
irregular, dynamic shear-banding and establish by decisive numerical tests that
the chaos we observe in the model is spatiotemporal in nature.
