Impact of noise and damage on collective dynamics of scale-free neuronal   networks
  We study the role of scale-free structure and noise in collective dynamics of neuronal networks. For this purpose, we simulate and study analytically a cortical circuit model with stochastic neurons. We compare collective neuronal activity of networks with different topologies: classical random graphs and scale-free networks. We show that, in scale-free networks with divergent second moment of degree distribution, an influence of noise on neuronal activity is strongly enhanced in comparison with networks with a finite second moment. A very small noise level can stimulate spontaneous activity of a finite fraction of neurons and sustained network oscillations. We demonstrate tolerance of collective dynamics of the scale-free networks to random damage in a broad range of the number of randomly removed excitatory and inhibitory neurons. A random removal of neurons leads to gradual decrease of frequency of network oscillations similar to the slowing-down of the alpha rhythm in Alzheimer's disease. However, the networks are vulnerable to targeted attacks. A removal of a few excitatory or inhibitory hubs can impair sustained network oscillations. 
D. Holstein, A. V. Goltsev, and J. F. F. Mendes
cond-mat.dis-nn physics.bio-ph q-bio.NC