  Neural systems process information in a dynamical regime between silence and
chaotic dynamics. This has lead to the criticality hypothesis which suggests
that neural systems reach such a state by self-organizing towards the critical
point of a dynamical phase transition. Here, we study a minimal neural network
model that exhibits self-organized criticality in the presence of stochastic
noise using a rewiring rule which only utilizes local information. For network
evolution, incoming links are added to a node or deleted, depending on the
node's average activity. Based on this rewiring-rule only, the network evolves
towards a critcal state, showing typical power-law distributed avalanche
statistics. The observed exponents are in accord with criticality as predicted
by dynamical scaling theory, as well as with the observed exponents of neural
avalanches. The critical state of the model is reached autonomously without
need for parameter tuning, is independent of initial conditions, is robust
under stochastic noise, and independent of details of the implementation as
different variants of the model indicate. We argue that this supports the
hypothesis that real neural systems may utilize similar mechanisms to
self-organize towards criticality especially during early developmental stages.
