Intralayer structure reconstruction of general weighted output-coupling multilayer complex networks

Multilayer complex dynamical networks, characterized by the intricate topological connections and diverse hierarchical structures, present significant challenges in determining complete structural configurations due to the unique functional attributes and interaction patterns inherent to different layers. This paper addresses the critical question of whether structural information from a known layer can be used to reconstruct the unknown intralayer structure of a target layer within general weighted output-coupling multilayer networks. Building upon the generalized synchronization principle, we propose an innovative reconstruction method that incorporates two essential components in the design of structure observers, the cross-layer coupling modulator and the structural divergence term. A key advantage of the proposed reconstruction method lies in its flexibility to freely designate both the unknown target layer and the known reference layer from the general weighted output-coupling multilayer network. The reduced dependency on full-state observability enables more deployment in engineering applications with partial measurements. Numerical simulations are conducted to validate the effectiveness of the proposed structure reconstruction method.