Towards designing robust coupled networks

Natural and technological interdependent systems have been shown to be highly vulnerable due to cascading and an abrupt collapse of global connectivity under initial failure. Mitigating the risk by partial endangers their functionality. Here we propose a systematic strategy of selecting a minimum of autonomous nodes that guarantee a smooth transition in robustness. Our method which is based betweenness is tested on various examples including the famous 2003 electrical blackout of Italy. We that, with this strategy, the necessary number of autonomous nodes can be reduced by a factor of five to a random choice. We also find that the transition to abrupt collapse follows tricritical scaling by a set of exponents which is independent on the protection strategy.