  We introduce a class of 1D models mimicking a single-lane bridge with two
junctions and two particle species driven in opposite directions. The model
exhibits spontaneous symmetry breaking (SSB) for a range of
injection/extraction rates. In this phase the steady state currents of the two
species are not equal. Moreover there is a co-existence region in which the
symmetry broken phase co-exists with a symmetric phase. Along a path in which
the extraction rate is varied, keeping the injection rate fixed and large,
hysteresis takes place. The mean field phase diagram is calculated and
supporting Monte-Carlo simulations are presented. One of the transition lines
exhibits a kink, a feature which cannot exist in transition lines of
equilibrium phase transitions.
