Mean first passage time of random walks on the generalized pseudofractal web

摘要

In this paper, we study the scaling for mean first passage time (MFPT) of random walks on the generalized pseudofractal web (GPFW) with a trap, where an initial state is transformed from a triangle to a r-polygon and every existing edge gives birth to finite nodes in the subsequent step. We then obtain an analytical expression and an exact scaling for the MFPT, which shows that the MFPT grows as a power-law function in the large limit of network order. In addition, we determine the exponent of scaling efficiency characterizing the random walks, with the exponent less than 1. The scaling exponent of the MFPT is same for the initial state of the web being a polygon with finite nodes. This method could be applied to other fractal networks.