Can dynamical synapses produce true self-organized criticality?

Neuronal networks can present activity described by power-law distributed avalanches presumed to be a signature of a critical state. Here we study a random-neighbor network of excitable cellular automata coupled by dynamical synapses. The model exhibits a very similar to conservative self-organized criticality (SOC) models behavior even with dissipative bulk dynamics. This occurs because in the stationary regime the model is conservative on average, and, in the thermodynamic limit, the probability distribution for the global branching ratio converges to a delta-function centered at its critical value. So, this non-conservative model pertain to the same universality class of conservative SOC models and contrasts with other dynamical synapses models that present only self-organized quasi-criticality (SOqC). Analytical results show very good agreement with simulations of the model and enable us to study the emergence of SOC as a function of the parametric derivatives of the stationary branching ratio.