  We present novel hysteretic behaviour of a three-level ladder atomic system
exhibiting double-cavity optical bistability in the mean-field limit. The two
fields coupling the atomic system experience feedback via two independent,
unidirectional, single mode ring cavities and exhibit cooperative phenomena,
simultaneously. The system displays a range of rich dynamical features varying
from normal switching to self pulsing and a period-doubling route to chaos for
both the fields. We focus our attention to a new hump like feature in the
bistable curve arising purely due to cavity induced inversion, which eventually
leads to negative hysteresis in the bistable response. This is probably the
only all-optical bistable system that exhibits positive as well as negative
bistable hysteresis in different input field intensity regimes. For both the
fields, the switching times, the associated critical slowing down, the
self-pulsing characteristics, and the chaotic behaviour can be controlled to a
fair degree, moreover, all these effects occur at low input light levels.
