Self-organized criticality in structured neural networks

Abstract

Critical self-organization has recently been reported in the neural networks in biological systems. It has been observed that the BTW on scale-free lattices with the degree distribution {$}p{_}d(k)\backslashsim k{^}{{}-\backslashgamma{\}}{$} fits the experiments. In this paper {$}p{_}d(k){$} is considered to be uniform in the interval {$}(0,n{_}0){$} and a maximum range of connection between nodes is considered (namely {$}R{$}). We numerically calculate the exponents of the distribution functions in terms of {$}(n{_}0,R){$}. Dijkstra radius is also defined for such systems to calculate the fractal dimension of the avalanches. The time dependence of the number of unstable nodes (NUN) is also investigated and it is numerically shown that it can not be continuously approach the regular lattice limit.