Approach to Failures in Complex Networks and Possible Interventions

Abstract

Complex networks form the backbone of modern infrastructure, including power grids, transportation and communication systems. While failures in such systems are often associated with external shocks or deliberate attacks, they can also arise spontaneously from the intrinsic fluctuations of the processes taking place within the network. This thesis investigates how such internal fluctuations can drive a complex network from normal operation to complete and irreversible failure. The work reveals that intrinsic fluctuations alone can lead to network collapse through three distinct regimes: independent failures, cascade failures, and overload failures. A capacity-to-load ratio is the parameter characterizing these regimes, with the same qualitative behavior observed across a range of network topologies, and real-world networks. The thesis further examines network recovery through delayed repair. The analysis demonstrates that early intervention, before the onset of cascading failures, is both more effective and less resource-intensive. In addition, structural and temporal signatures of approaching failure are identified, providing potential early-warning indicators of systemic collapse. Overall, this work establishes that large-scale network failure need not require an external perturbation: intrinsic stochastic fluctuations can themselves generate cascading breakdowns. The results provide a framework for understanding, anticipating, and mitigating failure in complex networked systems.