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Efficiency of long-range navigation on Treelike fractals

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  • Khajehnejad, Moein

Abstract

To get a deep understanding of a diffusion process and realizing the most efficient methods for investigating a real network, has always been of great interest and utility to us. In this work, we aim to study and compare our mobility in a network using a normal random walk and a long-range navigation strategy such as Lévy Walk. We study the Global Mean First Traverse Distance (GMFTD) and the entropy rate for this long-range navigation process and later, compare with a normal walk strategy. For this study, GMFTD is utilized instead of Global Mean First Passage Time (GMFPT). The reason for such a choice is the fact that for more accurate and precise results, we need to also take into account the cost of a large step in case of a long-range navigation strategy. Next, we continue by calculating the entropy rate in both procedures and we derive the corresponding expressions of these quantities on a Treelike fractal. Eventually, we show that while GMFTD decreases in a long-range navigation system, entropy rate will increase. We perform an analytical comparison between the two cases and clearly demonstrate the superiority of a Lévy Walk strategy. Eventually, our simulation results, based on the derived expressions, give us a very reliable estimation for the optimum value of exponent parameter, α, which are in strong agreement with each other for both cases of a minimum GMFTD and a maximum entropy rate.

Suggested Citation

  • Khajehnejad, Moein, 2019. "Efficiency of long-range navigation on Treelike fractals," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 102-110.
    • Handle: RePEc:eee:chsofr:v:122:y:2019:i:c:p:102-110
    DOI: 10.1016/j.chaos.2019.03.010
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    References listed on IDEAS

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    1. Zhongzhi Zhang & Alafate Julaiti & Baoyu Hou & Hongjuan Zhang & Guanrong Chen, 2011. "Mean first-passage time for random walks on undirected networks," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 84(4), pages 691-697, December.
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    3. Marta C. González & César A. Hidalgo & Albert-László Barabási, 2009. "Understanding individual human mobility patterns," Nature, Nature, vol. 458(7235), pages 238-238, March.
    4. Zhao, Yi & Weng, Tongfeng & Huang, Defeng (David), 2014. "Lévy walk in complex networks: An efficient way of mobility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 396(C), pages 212-223.
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