  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 are capable of receiving support via hyperedges. 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 salient discovery is that as the prevalence of
dependent nodes escalates, the system dynamics shift from a second-order to a
first-order phase transition. Notably, irrespective of the collapse pattern,
systems characterized by scale-free hyperdegree distributions within both
hypergraph layers consistently demonstrate superior robustness compared to
those adhering to Poisson hyperdegree distributions. In summary, our research
underscores the paramount significance of group support mechanisms and
intricate network topologies in determining the resilience of interconnected
systems against the propagation of cascading failures. By exploring the
interplay between these factors, we have gained insights into how systems can
be designed or optimized to mitigate the risk of widespread disruptions,
ensuring their continued functionality and stability in the face of adverse
events.
