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Mean first passage time for random walk on dual structure of dendrimer

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  • Li, Ling
  • Guan, Jihong
  • Zhou, Shuigeng

Abstract

The random walk approach has recently been widely employed to study the relations between the underlying structure and dynamic of complex systems. The mean first-passage time (MFPT) for random walks is a key index to evaluate the transport efficiency in a given system. In this paper we study analytically the MFPT in a dual structure of dendrimer network, Husimi cactus, which has different application background and different structure (contains loops) from dendrimer. By making use of the iterative construction, we explicitly determine both the partial mean first-passage time (PMFT, the average of MFPTs to a given target) and the global mean first-passage time (GMFT, the average of MFPTs over all couples of nodes) on Husimi cactus. The obtained closed-form results show that PMFPT and EMFPT follow different scaling with the network order, suggesting that the target location has essential influence on the transport efficiency. Finally, the impact that loop structure could bring is analyzed and discussed.

Suggested Citation

  • Li, Ling & Guan, Jihong & Zhou, Shuigeng, 2014. "Mean first passage time for random walk on dual structure of dendrimer," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 415(C), pages 463-472.
    • Handle: RePEc:eee:phsmap:v:415:y:2014:i:c:p:463-472
    DOI: 10.1016/j.physa.2014.08.029
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    Cited by:

    1. Zong, Yue & Dai, Meifeng & Wang, Xiaoqian & He, Jiaojiao & Zou, Jiahui & Su, Weiyi, 2018. "Network coherence and eigentime identity on a family of weighted fractal networks," Chaos, Solitons & Fractals, Elsevier, vol. 109(C), pages 184-194.

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