Topology identification in two-layer complex dynamical networks

This study focuses on topology identification in two-layer networks with peer-to-peer unidirectional couplings, where one layer (the response layer) receives information from the other layer (the drive layer). The goal is to construct a theoretical framework for identifying the topology of the response layer based on the dynamics observed in both layers. In particular, an auxiliary layer is constructed. Based on the LaSalle-type invariance principle, simple control inputs and updating laws are designed to enable nodes in the auxiliary layer to reach complete synchronization with their counterparts in the response layer. Simultaneously, the topology of the response layer is adaptively identified. Numerical simulations are conducted to illustrate the effectiveness of the method. The impact of the inter-layer information transmission speed on the identification performance is further investigated. It is revealed that neither too slow or too fast information transmission favors efficient identification, and there exists an optimal level of transmission speed. The duplex framework can model many real-world systems, such as communication-rumor spreading networks. Therefore, the method proposed in this study can spark attention and provide basic insights into further theoretical research and practical application of multilayer networks, including detecting spreading routes and locating sources of rumors or pseudo news.