  The combination of bistability and noise is ubiquitous in complex systems,
from biological to social interactions, and has important implications for
their functioning and resilience. We analyze a simple three-state model for
bistability in networks under varying unbiased noise. In a fully connected
network increasing noise yields a collapse of bistability to an unpolarised
state. In contrast, in complex networks noise can abruptly switch the
polarization state in an irreversible way. When two networks are combined
through increasing multiplex coupling, one is dominant and progressively
imposes its state on the other, offsetting or promoting the ability of noise to
switch polarization. Our results show that dynamical correlations and asymmetry
in dynamical processes in networks are sufficient for allowing unbiased noise
to produce abrupt irreversible transitions between extremes, which can be
neutralized or enhanced by multiplex coupling.
