THE AVERAGE TRAPPING TIME WITH NON-NEAREST-NEIGHBOR JUMPS ON THE LEVEL-3 SIERPINSKI GASKET

Abstract

In this paper, we consider the trapping problem on the level-3 Sierpinski gasket [Formula: see text] when both nearest-neighbor (NN) and non-nearest-neighbor (NNN) jumps are included. Based on the topological structure of network and the method of probability generation function, we get the analytical expression of the average trapping time (ATT). Therefore, compared with the case where only NN jumps are allowed, we modify the specific value of ATT. Our results prove the exponent of the scaling expression has nothing to do with the NNN jump probability [Formula: see text], i.e. the scaling expression of ATT still scales superlinearly with the large network size. According to the analytical expression, we do numerical simulations of ATT with respect to parameters [Formula: see text] and [Formula: see text] (the number of generations of the network). The results show that the ATT will decrease with the increase of [Formula: see text]. These also indicate that NNN jump is helpful to improve the efficiency of random walk on network [Formula: see text].