  It has been demonstrated that one of the most striking features of the
nervous system, the so called 'plasticity' (i.e high adaptability at different
structural levels) is primarily based on Hebbian learning which is a collection
of slightly different mechanisms that modify the synaptic connections between
neurons. The changes depend on neural activity and assign a special dynamic
behavior to the neural networks. From a structural point of view, it is an open
question what network structures may emerge in such dynamic structures under
'sustained' conditions when input to the system is only noise. In this paper we
present and study the `HebbNets', networks with random noise input, in which
structural changes are exclusively governed by neurobiologically inspired
Hebbian learning rules. We show that Hebbian learning is able to develop a
broad range of network structures, including scale-free small-world networks.
