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

Yun Chen, Zhizhuo Zhang and Bo Wu
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Yun Chen: School of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing 210023, P. R. China
Zhizhuo Zhang: ��School of Mathematics, Southeast University, Nanjing 210096, P. R. China
Bo Wu: School of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing 210023, P. R. China

FRACTALS (fractals), 2022, vol. 30, issue 01, 1-12

Abstract: In this paper, we consider the trapping problem on the level-3 Sierpinski gasket (SG3) 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 q, 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 q and n (the number of generations of the network). The results show that the ATT will decrease with the increase of q. These also indicate that NNN jump is helpful to improve the efficiency of random walk on network SG3.

Keywords: Average Trapping Time; Non-Nearest-Neighbor Jumps; Level-3 Sierpinski Gasket (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X21502364

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