Recent studies have shown that adaptive networks driven by simple local rules URLanize into "critical" global steady states, thereby providing another framework for URLanized criticality (SOC). We focus on the important convergence to criticality and demonstrate 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. As a novel paradigm for adaptive networks SOC, we suggest to investigate each of the three new effects separately by developing models. These models reveal three generically possible low-dimensional dynamical behaviors: time-scale resonance (TR), a new simplified version of stochastic resonance - which  call steady state stochastic resonance (SSR) - as well as noise-induced phase transitions . Thereby, our study not only opens up new directions for optimality in SOC but also applies to a very wide class of dynamical systems .
Recent studies have shown that adaptive networks driven by simple local rules URLanize into "critical" global steady states, providing another framework for URLanized 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 .
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As a novel paradigm for adaptive networks SOC, we suggest to
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possible
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. Thereby, our study not only opens up new directions for optimality in SOC but also applies to a very wide class of dynamical systems