Scaling laws of failure dynamics on complex networks

Abstract

The topology of the network of load transmitting connections plays an essential role in the cascading failure dynamics of complex systems driven by the redistribution of load after local breakdown events. In particular, as the network structure is gradually tuned from regular to completely random a transition occurs from the localized to mean field behavior of failure spreading. Based on finite size scaling in the fiber bundle model of failure phenomena, here we demonstrate that outside the localized regime, the load bearing capacity and damage tolerance on the macro-scale, and the statistics of clusters of failed nodes on the micro-scale obey scaling laws with exponents which depend on the topology of the load transmission network and on the degree of disorder of the strength of nodes. Most notably, we show that the spatial structure of damage governs the emergence of the localized to mean field transition: as the network gets gradually randomized failed clusters formed on locally regular patches merge through long range links generating a percolation like transition which reduces the load concentration on the network. The results may help to design network structures with an improved robustness against cascading failure.

arXiv comment14 pages, 7 figures

References in corpus (29)

• Epidemic processes in complex networks
• The spread of epidemic disease on networks
• Spatial Networks
• Scaling and percolation in the small-world network model
• Epidemics and percolation in small-world networks
• Statistical Models of Fracture
• Failure Processes in Elastic Fiber Bundles
• Instability of scale-free networks under node-breaking avalanches
• Tri-critical behavior in rupture induced by disorder
• Burst avalanches in solvable models of fibrous materials
• Fracture model with variable range of interaction
• Size effects in statistical fracture
• Shortest paths on systems with power-law distributed long-range connections
• Role of disorder in the size-scaling of material strength
• Temporal profiles of avalanches on networks
• Griffiths phases and localization in hierarchical modular networks
• Robustness of power systems under a democratic fiber bundle-like model
• Modes of failures in disordered solids
• Temporal and spacial evolution of bursts in creep rupture
• Time evolution of damage under variable ranges of load transfer
• Phase transitions in Ising model on a Euclidean network
• A Fiber Bundle Model of Traffic Jams
• The Local load sharing fiber bundle model in higher dimensions
• Heterogeneous excitable systems exhibit Griffiths phases below hybrid phase transitions
• Breakdown of fiber bundles with stochastic load-redistribution
• Avalanche dynamics in higher dimensional fiber bundle models
• Transition from localized to mean field behaviour of cascading failures in the fiber bundle model on complex networks
• Micro-structure of damage in thermally activated fracture of Lennard-Jones systems
• Mesoscopic Description of the Equal Load Sharing Fiber Bundle Model