  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
the three new effects separately by developing models. These models reveal
three generically low-dimensional dynamical behaviors: time-scale resonance
(TR), a new simplified version of stochastic resonance - which we call steady
state stochastic resonance (SSR) - as well as noise-induced phase transitions.
