  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.
