Christian M. Schneider, Nuri Yazdani, Nuno A. M. Araujo, Shlomo Havlin, Hans J. Herrmann
Natural and technological interdependent systems are highly vulnerable due to dependencies which pose a huge integrative risk due to the recently discovered abrupt collapse under failure. Mitigating the risk by partial disconnection endangers their functionality. Here we propose a systematic strategy of establishing a minimum number of autonomous nodes that guarantee a smooth transition in the robustness. Our method which is based on betweenness is tested on various examples including the famous 2003 electrical blackout of Italy. We show that we can reduce the necessary number of autonomous nodes by a factor of five compared to the random choice which for practical purposes means the recovery of functionality. We also find that the transition to abrupt collapse follows tricritical scaling characterized by a set of exponents which is independent on the protection strategy.
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http://arxiv.org/abs/1106.3234
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