Distributed Adaptive Algorithms for Intralayer Synchronization of Multiplex Networks

This article investigates distributed adaptive algorithms for intralayer synchronization of multiplex networks, both with and without pinning control. Two types of distributed adaptive algorithms are considered based on the parameters being adjusted: 1) node-based algorithms, which adapt the coupling strength of each node using the relative information from its neighborhood and itself, and 2) edge-based algorithms, which update the coupling weight of each edge based on the relative information between the two connected nodes. Using the Lyapunov function method, we prove that, under mild conditions on the uncoupled node dynamics, the proposed adaptive strategies guarantee intralayer synchronization for any multiplex network with strongly connected intralayer topologies.