Coupled Map Lattice Modeling and Robustness Analysis of Simplicial Complex Networks with Higher-Order Interactions

Cascading failures in complex networks occur when local node or edge failures propagate to trigger large-scale collapse. Traditional pairwise network models cannot adequately capture group coordination and multi-agent higher-order interactions. Higher-order networks incorporating simplicial structures more accurately represent group and multi-node interactions, providing a new framework to study cascading failures and network robustness. The paper proposes a higher-order coupled map lattice (CML) model to characterize cascading failures in simplicial complex networks and analyze the influence of higher-order structures on network robustness. Further experiments on fourth-order simplicial networks investigate robustness differences under various topologies and attack strategies. Results indicate that fourth-order simplicial networks are vulnerable to targeted attacks but robust against random failures, regardless of network type. Furthermore in single-order networks, the higher simplex dimensions, the greater robustness. The theoretical perturbation thresholds for third-order networks show a negative correlation between the critical perturbation and the sum of network coupling parameters. These results are validated by analysis of simplices added to ordinary networks, destructive experiments, and empirical networks. This study deepens the understanding of cascading failure mechanisms and robustness in higher-order networks, and provides theoretical guidance for designing resilient networks based on higher-order structures.