  We study a simple model of shear banding in which the flow-induced phase is
destabilised by coupling between flow and microstructure (wormlike micellar
length). By varying the strength of the instability and the applied shear rate,
we find a rich variety of oscillatory and rheochaotic shear banded flows. At
low shear and weak instability, the induced phase pulsates in width next to one
wall of the flow cell. For stronger instability, single or multiple high shear
pulses ricochet across the cell. At high shear rates we observe oscillating
bands on either side of a defect. In some cases, multiple such defects exist
and propagate across the cell to interact with each other. We discuss our
results in the context of recent observations of oscillating and fluctuating
shear banded flows.
