Self-organized Criticality and Scale-free Properties in Emergent   Functional Neural Networks
  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. 
Chang-Woo Shin and Seunghwan Kim