Cascading dynamics in double-layer hypergraphs with higher-order inter-layer interdependencies

Higher-order interactions are ubiquitous in complex systems where groups of elements interact collectively rather than through simple pairwise connections. This study investigates how higher-order inter-layer interdependencies affect the robustness and cascading dynamics in double-layer hypergraphs, in which groups of nodes in one layer are interdependent with groups of nodes in the other layer. We analyze how the average size of these interdependency groups across layers influences system robustness and the nature of phase transitions. First, as the average size of higher-order inter-layer interdependency groups increases, the system undergoes a change from a second-order to a first-order phase transition. Second, in scale-free hypergraphs, larger interdependency groups can cause two consecutive first-order transitions, indicating nontrivial dynamical behavior that may affect the predictability and controllability of the system. Finally, the impact of higher-order inter-layer interdependencies on system robustness is not straightforward, i.e., it does not monotonically increase or decrease across both scale-free and random hypergraphs. Specifically, intermediate-sized interdependency groups result in the most vulnerable system, as indicated by the highest critical point for system disintegration. These results give useful views into how multilayer network architectures with higher-order interdependencies affect the resilience and stability of interconnected systems, offering practical guidance for designing more robust infrastructure networks.