Pinning intra-layer synchronization in multiplex networks of nonidentical layers

In this paper, we investigate intra-layer synchronization in multiplex networks via pinning control strategies. All layers have different topologies and different intrinsic node dynamics. Novel sufficient criteria are derived for pinning intra-layer synchronization of multiplex networks, which indicates that the pinned node set can stabilize the multiplex network if, for each layer, the pinned node(s) can access all unpinned nodes. A distributed adaptive algorithm and finite-time pinning algorithm for intra-layer synchronization of multiplex networks are also proposed. Finally, we give some numerical examples to validate the effectiveness of these theoretical results.