  Nonlinear complex network-coupled systems typically have multiple stable
equilibrium states. Following perturbations or due to ambient noise, the system
is pushed away from its initial equilibrium and, depending on the direction and
the amplitude of the excursion, might undergo a transition to another
equilibrium. It was recently demonstrated [M. Tyloo, J. Phys. Complex. 3 03LT01
(2022)], that layered complex networks may exhibit amplified fluctuations. Here
I investigate how noise with system-specific correlations impacts the first
escape time of nonlinearly coupled oscillators. Interestingly, I show that, not
only the strong amplification of the fluctuations is a threat to the good
functioning of the network, but also the spatial and temporal correlations of
the noise along the lowest-lying eigenmodes of the Laplacian matrix. I analyze
first escape times on synthetic networks and compare noise originating from
layered dynamics, to uncorrelated noise.
