Inter-layer Generalized Synchronization for Fractional-Order Two-Layer Networks Based on Auxiliary-System Method

This paper focuses on investigating inter-layer generalized synchronization for fractional-order two-layer networks, the two layers in which have nonidentical node dynamics, different topologies, and unknown functional relationships. On the basis of the auxiliary-system method, an auxiliary system is constructed, specifically, the auxiliary system and the response (bottom) layer receive the same control inputs from the drive (top) layer. In addition, the adaptive controllers are designed to ensure the bottom layer and the auxiliary layer to realize complete synchronization. The top layer achieves inter-layer generalized synchronization with the bottom layer simultaneously. Eventually, numerical examples are conducted to verify the effectiveness of our established synchronization method.