Non-Markovian node fragility in cascading failures on random networks

Abstract

The memory effect of node fragility plays an important role in determining the cascading dynamics of complex systems. This paper focuses on the impact of non-Markovian characteristics of cascading dynamics on system robustness, where the fragility of each node evolves with the increase of failed neighbors and governs the failure probability of the node. The research reveals that the rate of change in node fragility not only impacts the critical point of the system’s phase transition but also influences the manner in which the system collapses. Notably, the collapse patterns of the system can exhibit first-order, second-order, or double-phase transitions. Additionally, the initial fragility of nodes has a great impact on the occurrence of cascading failures. Specifically, when the initial fragility of nodes exceeds the inverse of the mean degree, the network experiences an abrupt collapse even with the removal of an infinitesimally small fraction of nodes, regardless of memory effects. The findings provide profound insights into the intricate interplay between dependent relationships and memory effects during cascading failure processes. Furthermore, it offers a deep understanding for effectively assessing the vulnerability of complex systems and devising strategies to mitigate cascading failures.