Trapping on deterministic multiplex networks

We study the trapping problem associated with a random walk process that takes place in deterministic multiplex networks. To this end, we consider the Average Trapping Time (ATT) and explore the properties of this system by adjusting the coupling strength λ. We get the analytical expression of ATT with the help of the properties of block matrix, and apply it to two types of deterministic multiplex networks. We find that the ATT in our examples presents a minimum with the change of λ and that the emergence of the minimum under some special initial conditions has a potential relationship with the structural difference of the two graphs in the multiplex network. Our results provide a potential way to control the trapping time in multiplex networks.