  Effects of feedbacks on self-organization phenomena in networks of
diffusively coupled bistable elements are investigated. For regular trees, an
approximate analytical theory for localized stationary patterns under
application of global feedbacks is constructed. Using it, properties of such
patterns in different parts of the parameter space are discussed. Numerical
investigations are performed for large random Erd\"os-R\'enyi and scale-free
networks. In both kinds of systems, localized stationary activation patterns
have been observed. The active nodes in such a pattern form a subnetwork, whose
size decreases as the feedback intensity is increased. For strong feedbacks,
active subnetworks are organized as trees. Additionally, local feedbacks
affecting only the nodes with high degrees (i.e. hubs) or the periphery nodes
are considered.
