Localized modes and bistable scattering in nonlinear network junctions

We study the properties of junctions created by crossing of N identical branches of linear discrete networks. We reveal that for N>2 such a junction creates a topological defect and supports two types of spatially localized modes. We analyze the wave scattering by the junction defect and demonstrate nonzero reflection for any set of parameters. If the junction is nonlinear, it is possible to achieve the maximum transmission for any frequency by tuning the intensity of the scattering wave. In addition, near the maximum transmission the system shows the bistable behaviour.