Critical behavior of cascading failures in overloaded networks

Abstract

In recent years, research on spatial networks has become of widespread interest, with the focus on analyzing critical phenomena that can dramatically affect real systems via cascading failures and abrupt collapses. Here, we study the breakdown of a spatial network having a characteristic link-length due to overloads and the cascading failures that are triggered by failures of a fraction of links. While such breakdowns have been studied extensively, the critical exponents and the universality class of this phase transition have not been found. Here, we show indications that this transition has features and critical exponents which are the same as those of interdependent network systems, suggesting that both systems are in the same universality class. We find different abrupt transitions at the steady state, for different spatial embedding strength. For the weakly embedded systems (i.e., link-lengths of the order of the system size) we observe a mixed-order transition where the order parameter collapses with time in a long plateau shape. On the other hand, in strongly embedded systems (relatively short links), we find a pure first order transition which involves nucleation and growth of damage. System behavior in both limits is analogous to that observed in interdependent networks.