Cascading failures with group support in interdependent hypergraphs

The functionality of an entity frequently necessitates the support of a group situated in another layer of the system. To unravel the profound impact of such group support on a system’s resilience against cascading failures, we devise a framework comprising a double-layer interdependent hypergraph system, wherein nodes in one layer are capable of receiving support via hyperedges in another layer. Our central hypothesis posits that the failure may transcend to another layer when all support groups of each dependent node fail, thereby initiating a potentially iterative cascade across layers. Through rigorous analytical methods, we derive the critical threshold for the initial node survival probability that marks the second-order phase transition point. A notable finding is that as the proportion of dependent nodes increases, the dynamics of the double-layer system, characterized by Poisson hyperdegree distributions, transition from exhibiting a second-order phase transition to a first-order phase transition. In summary, our research highlights the critical role of group support mechanisms and intricate network topologies in influencing the resilience of interconnected systems with higher-order interactions against cascading failures, providing valuable insights for designing or optimizing systems to mitigate widespread disruptions and ensure sustained functionality and stability under adverse conditions.