Synchronization in multiplex networks

Synchronization in a network of connected elements is essential to the proper functioning of both natural and engineered systems and is thus of increasing interest across disciplines. In many cases, synchronization phenomena involve not just actions within a single network in isolation, but the coordinated and coherent behaviors of several networks interacting with each other. The interactions between multiple systems play a crucial role in determining the emergent dynamics. One paradigm capable of representing real-world complex systems is that of multiplex networks, where the same set of nodes exists in multiple layers of the network. Recent studies have made significant progress in understanding synchronization in multiplex networks. In this review, we primarily focus on two key aspects: structural complexity and dynamical complexity. From the perspective of structural complexity, we present how the topological setting, such as the interlayer coupling pattern, affects the synchronizability of a multiplex network. The structural characteristics of a multiplex network, in particular, give rise to dynamical complexity, including the emergence of intralayer synchronization (within each layer) and interlayer synchronization (between layers). We also discuss the major methods for studying the stability of complete, intralayer, and interlayer synchronization, as well as synchronization control in multiplex networks. Additionally, we briefly introduce some relevant applications. Lastly, the review provides a comprehensive summary of the notable findings in the study of synchronization in multiplex networks, emphasizing the interplay between their structural and dynamical complexities, and identifies open problems that present opportunities for future research in this field.