Time-scale and noise optimality in self-organized critical adaptive networks.

Recent studies have shown that adaptive networks driven by simple local rules can organize into "critical" global steady states, providing another framework for self-organized criticality (SOC). We focus on the important convergence to criticality and show that noise and time-scale optimality are reached at finite values. This is in sharp contrast to the previously believed optimal zero noise and infinite time-scale separation case. Furthermore, we discover a noise-induced phase transition for the breakdown of SOC. We also investigate each of these three effects separately by developing models that reveal three generically low-dimensional dynamical behaviors: time-scale resonance, a simplified version of stochastic resonance, which we call steady-state stochastic resonance, and noise-induced phase transitions.