  Networks of interacting, communicating subsystems are common in many fields,
from ecology, biology, epidemiology to engineering and robotics. In the
presence of noise and uncertainty, inter- actions between the individual
components can lead to unexpected complex system-wide behaviors. In this paper,
we consider a generic model of two weakly coupled dynamical systems, and show
how noise in one part of the system is transmitted through the coupling
interface. Working synergistically with the coupling, the noise on one system
drives a large fluctuation in the other, even when there is no noise in the
second system. Moreover, the large fluctuation happens while the first system
exhibits only small random oscillations. Uncertainty effects are quantified by
showing how characteristic time scales of noise induced switching scale as a
function of the coupling between the two coupled parts of the experiment. In
addition, our results show that the probability of switching in the noise-free
system scales inversely as the square of reduced noise intensity amplitude,
rendering the virtual probability of switching to be an extremely rare event.
Our results showing the interplay between transmitted noise and coupling are
also confirmed through simulations, which agree quite well with analytic
theory.
