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). Here we study SOC in an adaptive network considered first by Bornholdt and Rohlf PRL, 84(26), p.6114-6117, 2000%DIFDELCMD < ]%%% . We focus on the important convergence to criticality and discover time-scale and noise optimal behaviour as well as a noise-induced phase transition . Due to the complexity of adaptive networks dynamics we suggest to investigate each effect separately by developing simple models. These models reveal three generically possible low-dimensional dynamical behaviors: time-scale resonance (TR), a  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 much wider class of dynamical systems.
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). %DIFDELCMD < ]%%% 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.
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Here we study SOC in an adaptive network considered first by Bornholdt and Rohlf
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PRL, 84(26), p.6114-6117, 2000
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