Collective synchronization of two-layer Kuramoto-oscillator network with different architectures

Abstract The topic of multi-layer networks has received considerable attention in recent years. However, most existing studies are based on idealized assumptions, such as identical type of intra-layer topologies and one-to-one inter-layer connections, which fail to reflect the heterogeneity and flexibility observed in real-world networks like brain neural activities and power grids. To address these limitations, this study investigates the synchronization dynamics of a two-layer Kuramoto network with distinct topologies, unequal node counts, and flexible random inter-layer connections. Using numerical simulations, we analyze how structural asymmetries and flexible inter-layer connections influence synchronization. Our findings reveal that: (1) for identical type of network topologies, the layer with more nodes is less influenced by the other layer as coupling strength increases; (2) distinct network topologies show different synchronization rates; (3) when the number of nodes in one layer is fixed and in the other increases (with the layer having more nodes randomly connecting to the layer with fewer nodes), the layer with fewer nodes synchronizes more easily, while partial synchronization occurs in the other layer, in the inter-layer connections, and across the entire network; (4) the difference in node counts in two-layer networks can facilitate synchronization.