  Recent studies on the complex systems have shown that the synchronization of
oscillators including neuronal ones is faster, stronger, and more efficient in
the small-world networks than in the regular or the random networks, and many
studies are based on the assumption that the brain may utilize the small-world
and scale-free network structure. We show that the functional structures in the
brain are self-organized to both the small-world and the scale-free networks by
synaptic re-organization by the spike timing dependent synaptic plasticity
(STDP), which is hardly achieved with conventional Hebbian learning rules. We
show that the balance between the excitatory and the inhibitory synaptic inputs
is critical in the formation of the functional structure, which is found to lie
in a self-organized critical state.
