Analytical investigation of self-organized criticality in neural networks

Dynamical criticality has been shown to enhance information processing in dynamical systems, and there is evidence for self-organized criticality in neural networks. A plausible mechanism for such self-organization is activity-dependent synaptic plasticity. Here, we model neurons as discrete-state nodes on an adaptive network following stochastic dynamics. At a threshold connectivity, this system undergoes a dynamical phase transition at which persistent activity sets in. In a low-dimensional representation of the macroscopic dynamics, this corresponds to a transcritical bifurcation. We show analytically that adding activity-dependent rewiring rules, inspired by homeostatic plasticity, leads to the emergence of an attractive steady state at criticality and present numerical evidence for the system's evolution to such a state.