Range of shortcuts in the dynamic model of neural networks

We study, via extensive Monte Carlo calculations, the effects of the range of shortcuts in the dynamic model of neural networks. With the increase of the range of shortcuts, the Mattis-state order parameter grows and the ordered-state region expands in the phase diagram, encroaching upon the mixed-phase region in the phase diagram. In particular, the power spectra of the order parameter at stationarity are observed to exhibit different shapes, depending on the range of shortcuts in the network. The cluster size distribution of the memory-unmatched sites, as well as the distribution of waiting times for neuron firing, possesses strong correlations with the power spectra in their shapes, all exhibiting the most pronounced power-law behaviors when the range of shortcuts is long.