Determining average trapping time of delayed random walks on Apollonian network

Abstract

Designing appropriate technology to effectively control the trapping process in complex systems and achieve the desired trapping efficiency is central in the study of trapping problem in complex systems. In this paper, we study delayed random walks on Apollonian network with a trap fixed at a given initial hub node. In more detail, a stochastic parameter p was introduced in the approach to alter the transition probability of random walks. We further derive analytically the average trapping time (ATT) as the measure of trapping efficiency with the obtained analytical expression being in good agreement with the corresponding numerical solutions. The result indicates that ATT scales sublinearly with network size when [Formula: see text]. Therefore, we introduced stochastic parameter p only alter the prefactor of ATT and left the leading scaling of ATT unchanged. Our work may pave the way for understanding how to control trapping process in real complex systems.