Uncovering the impact of delay phenomenon on random walks in a family of weighted m-triangulation networks

Abstract

Uncovering the impact of special phenomena on dynamical processes in more distinct weighted network models is still needed. In this paper, we investigate the impact of delay phenomenon on random walk by introducing delayed random walk into a family of weighted m-triangulation networks. Specifically, we introduce delayed random walk into the networks. Then one and three traps are deployed, respectively, on the networks in two rounds of investigation. In both rounds of investigation, average trapping time (ATT) is applied to measure trapping efficiency and derived analytically by harnessing iteration rule of the networks. The analytical solutions of ATT obtained in both investigations show that ATT increases sub-linearity with the size of the network no matter what value the parameter [Formula: see text] manipulating delayed random walk takes. But [Formula: see text] can quantitatively change both its leading scaling and prefactor. So, introduction of delay phenomenon can control trapping efficiency quantitatively. Besides, parameters [Formula: see text] and [Formula: see text] governing networks’ evolution quantitatively impact both the prefactor and leading scaling of ATT simultaneously. In summary, this work may provide incremental insight into understanding the impact of observed phenomena on special trapping process and general random walks in complex systems.