Critical behavior of cascading failures in overloaded networks

Abstract

While network abrupt breakdowns due to overloads and cascading failures have been studied extensively, the critical exponents and the universality class of such phase transitions have not been discussed. Here, we study breakdowns triggered by failures of links and overloads in networks with a spatial characteristic link length $\zeta$. Our results indicate that this abrupt transition has features and critical exponents similar to those of interdependent networks, suggesting that both systems are in the same universality class. For weakly embedded systems (i.e., $\zeta$ of the order of the system size $L$) we observe a mixed-order transition, where the order parameter collapses following a long critical plateau. On the other hand, strongly embedded systems (i.e., $\zeta \ll L$) exhibit a pure first-order transition, involving nucleation and the growth of damage. The system's critical behavior in both limits is similar to that observed in interdependent networks.

arXiv comment6 pages, 6 figures

References in corpus (11)

• Catastrophic cascade of failures in interdependent networks
• Spatial Networks
• Cascade-based attacks on complex networks
• Cascade control and defense in complex networks
• Explosive transitions in complex networks' structure and dynamics: percolation and synchronization
• Spatially localized attacks on interdependent networks: the existence of a finite critical attack size
• Two distinct transitions in spatially embedded multiplex networks
• Spreading of localized attacks in spatial multiplex networks
• Fractal fluctuations at mixed-order transitions in interdependent networks
• Percolation on spatial anisotropic networks
• Cascading failures in isotropic and anisotropic spatial networks induced by localized attacks and overloads