  We present a numerical study of multi-commodity transport in a noisy,
nonlinear network. The nonlinearity determines the dynamics of the edge
capacities, which can be amplified or suppressed depending on the local current
flowing across an edge. We consider network self-organization for three
different nonlinear functions: For all three we identify parameter regimes
where noise leads to self-organization into more robust topologies, that are
not found by the sole noiseless dynamics. Moreover, the interplay between noise
and specific functional behavior of the nonlinearity gives rise to different
features, such as (i) continuous or discontinuous responses to the demand
strength and (ii) either single or multi-stable solutions. Our study shows the
crucial role of the activation function on noise-assisted phenomena.
