RANDOM WALKS WITH A TRAP IN SCALE-FREE FRACTAL HIERARCHICAL LATTICES

Abstract

In this paper, we study two kinds of random walks with a trap in a class of scale-free fractal hierarchical lattices. One is standard random walks belonging to unbiased random walks, while the other one named mixed random walks is biased. The structural properties of these hierarchical lattices are controlled by a parameter [Formula: see text]. We derive exact solutions of the average trapping time (ATT) for the two trapping issue, respectively. The results show that in large networks, both of the ATT grow asymptotically as a power-law function of network size with the exponent related to the parameter [Formula: see text]. It indicates that network structure has a substantial effect on the efficiency of trapping processes performed in scale-free networks. Comparing the results obtained for the two different random walks, we find that changes of the walking rule have no effect on the leading exponent of the ATT, but could modify the coefficient of the formula for the ATT. The findings are helpful for better understanding the influence factor of random walks in complex systems.