Spreading of failures in interdependent networks

Deviating from the common situation where some physical objects are considered to move in space, the present chapter deals with the spreading of failures in complex systems like power grids, communications networks and financial networks. Failures can trigger a cascade of further failures that spread to other parts of the system with, possibly, dramatic consequences and catastrophic events like blackouts and economic collapses. The focus of this chapter is on the specific mechanisms occurring in interdependent systems, where components of one system cannot function without components of the other, as in the case of a communication tower which needs power from the nearby power station. Understanding how these failures spread in both time and space is critical for ensuring that large-scale complex systems remain functional. A further challenge examined here involves the question of how to optimally repair and recover a system after it has experienced some failures—for preventing quick failure reappearance in the repaired components.