MEAN TIME TO ABSORPTION ON THE JOINT SIERPINSKI GASKET

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

FRACTALS (fractals), 2021, vol. 29, issue 04, 1-17

Abstract: As a kind of classical fractal network models, Sierpinski Gasket and its extended network models have attracted the attention of many scholars because of their many applications in real-world networks. Based on the classical Sierpinski Gasket, this paper proposes a joint Sierpinski Gasket model, which can be used not only to study the topology and dynamic properties of Sierpinski Gasket itself, but also to study the Sierpinski Gasket under special conditions, such as the residual Sierpinski Gasket after damage. Since the mean time to absorption (MTA) on the network is a basic dynamic property related to the random walk, in this paper, we study the expression of MTA on the proposed general joint Sierpinski Gasket model, and find that the MTA is determined by the number of iterations g and two variables determined by the mode variable S, which can be solved by matrix algorithm. Therefore, using the expression of MTA on the general joint Sierpinski Gasket model, we calculate the analytical expressions of the MTA on a general example of the joint Sierpinski Gasket model and three Sierpinski Gaskets with varying degrees of damage and do the corresponding numerical simulation to verify the correctness of the conclusion.

Keywords: Random Walk; Mean Time to Absorption; Self-Similar Networks; Sierpinski Gasket; Joint Sierpinski Gasket Model (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S0218348X2150078X

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