Cascading failure analysis of uniform double-layer hyper-networks based on the Couple Map Lattice model

Cascading failures are a class of dynamical behaviors that are widely present in various types of complex systems. The study of cascading failures has also been a hot topic for researchers. The results have shown that the process of cascading failures varies greatly depending on the structure of the network. Based on the double-layer hyper-network structure, considering the types of hyper-networks and the way of inter-layer connection, we construct four types of 3 uniform double-layer hyper-networks. In addition, the Couple Map Lattice (CML) cascading failure model is proposed which is suitable for describing the cascading failure behavior of a double-layer hyper-network. By this model, we analyzed the cascading failure processes happen in hyper-edges of a uniform double-layer hyper-network. Furthermore, through theoretical analysis, an approximate solution for the external perturbation threshold is obtained, which makes the double-layer hyper-network reaches the global collapse. The results of this paper provide an important reference for optimizing the robustness of realistic double-layer hyper-networks. In practical applications, the robustness of the double-layer hyper-networks can be improved by reducing the inter-layer connectivity probability
$p12$
and the coupling strength
$\varepsilon$
between hyper-edges.