Research PaperNo Access

Uncovering the impact of delay phenomenon on random walks in a family of weighted m-triangulation networks

Junhao Guo

Business School, University of Shanghai for Science and Technology, Shanghai 200093, P. R. China

E-mail Address: [email protected]

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and

Zikai Wu

https://orcid.org/0000-0002-7295-8053

Business School, University of Shanghai for Science and Technology, Shanghai 200093, P. R. China

E-mail Address: [email protected]

Corresponding author.

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https://doi.org/10.1142/S0217979221502349Cited by:0 (Source: Crossref)

Abstract

Uncovering the impact of special phenomena on dynamical processes in more distinct weighted network models is still needed. In this paper, we investigate the impact of delay phenomenon on random walk by introducing delayed random walk into a family of weighted m-triangulation networks. Specifically, we introduce delayed random walk into the networks. Then one and three traps are deployed, respectively, on the networks in two rounds of investigation. In both rounds of investigation, average trapping time (ATT) is applied to measure trapping efficiency and derived analytically by harnessing iteration rule of the networks. The analytical solutions of ATT obtained in both investigations show that ATT increases sub-linearity with the size of the network no matter what value the parameter $p$ manipulating delayed random walk takes. But $p$ can quantitatively change both its leading scaling and prefactor. So, introduction of delay phenomenon can control trapping efficiency quantitatively. Besides, parameters $h$ and $m$ governing networks’ evolution quantitatively impact both the prefactor and leading scaling of ATT simultaneously. In summary, this work may provide incremental insight into understanding the impact of observed phenomena on special trapping process and general random walks in complex systems.

Keywords:

PACS: 05.40.Fb, 05.45.Fb

References

1. S. Wang and C. Zhang, Phys. Rev. E 70, 066127 (2004). Crossref, Web of Science, ADS, Google Scholar
2. K. Klemm and V. M. Eguluz, Phys. Rev. E 65, 057102 (2002). Crossref, Web of Science, ADS, Google Scholar
3. D. J. Watts and S. H. Strogatz, Nature 393, 440 (1998). Crossref, Web of Science, ADS, Google Scholar
4. D. H. Damian, Phys. Rev. E 65, 4 (2002). Google Scholar
5. A. B. Haim, J. A. Klafter and R. Kopelman, J. Am. Chem. Soc. 119, 6197 (1997). Crossref, Web of Science, Google Scholar
6. J. L. Bentz and J. J. Kozak, J. Lumin. 121, 62 (2006). Crossref, Web of Science, Google Scholar
7. B. Wu et al., J. Chem. Phys. 137, 044903 (2012). Crossref, Web of Science, Google Scholar
8. Y. Lin and Z. Z. Zhang, J. Chem. Phys. 138, 094905 (2013). Crossref, Web of Science, Google Scholar
9. E. Agliari, Phys. Rev. E 77, 011128 (2008). Crossref, Web of Science, ADS, Google Scholar
10. B. Kahng and S. Redner, Phys. A 22, 887 (1989). Crossref, Web of Science, ADS, Google Scholar
11. C. P. Haynes and A. P. Roberts, Phys. Rev. E 78, 041111 (2008). Crossref, Web of Science, ADS, Google Scholar
12. Y. Lin, B. Wu and Z. Z. Zhang, Phys. Rev. E 82, 031140 (2010). Crossref, Web of Science, ADS, Google Scholar
13. Z. Z. Zhang, B. Wu and G. R. Chen, Europhys. Lett. 96, 40009 (2011). Crossref, ADS, Google Scholar
14. J. H. Peng and G. A. Xu, J. Chem. Phys. 140, 134102 (2014). Crossref, Web of Science, ADS, Google Scholar
15. J. J. Kozak and V. Balakrishnan, Phys. Rev. E 65, 021105 (2002). Crossref, Web of Science, ADS, Google Scholar
16. J. J. Kozak and V. Balakrishnan, Int. J. Bifurcat. Chaos 12, 2379 (2002). Link, Web of Science, Google Scholar
17. J. L. Bentz, J. W. Turner and J. J. Kozak, Phys. Rev. E 82, 011137 (2010). Crossref, Web of Science, ADS, Google Scholar
18. Z. Z. Zhang, L. L. Rong and S. G. Zhou, Phys. A 377, 329 (2007). Crossref, Web of Science, ADS, Google Scholar
19. E. Agliari, R. Burioni and A. Manzotti, Phys. Rev. E 82, 011118 (2010). Crossref, Web of Science, ADS, Google Scholar
20. H. J. Peng, J. Xiong and G. A. Xu, Phys. A 407, 231 (2014). Crossref, Web of Science, ADS, Google Scholar
21. Z. Z. Zhang et al., Phys. Rev. E 79, 061113 (2009). Crossref, Web of Science, ADS, Google Scholar
22. Z. Z. Zhang et al., Eur. Phys. J. B 64, 277 (2008). Crossref, Web of Science, ADS, Google Scholar
23. M. E. J. Newman, SIAM Rev. 45, 167 (2003). Crossref, Web of Science, ADS, Google Scholar
24. L. M. Pecora and T. L. Carroll, Phys. Rev. Lett. 80, 2109 (1998). Crossref, Web of Science, ADS, Google Scholar
25. A. L. Lloyd and R. M. May, Science 292, 1316 (2001). Crossref, Web of Science, Google Scholar
26. F. Jasch and A. Blumen, Phys. Rev. E 63, 041108 (2001). Crossref, Web of Science, ADS, Google Scholar
27. S. Redner, Am. J. Phys. 70, 1166 (2002). Crossref, ADS, Google Scholar
28. S. K. Kim, J. Chem. Phys. 28, 1057 (1958). Crossref, Web of Science, ADS, Google Scholar
29. Y. Lin and Z. Z. Zhang, Sci. Rep. 4, 6274 (2014). Crossref, Web of Science, Google Scholar
30. V. Balakrishnan and J. J. Kozak, Phys. Rev. E 88, 052139 (2013). Crossref, Web of Science, ADS, Google Scholar
31. Z. Z. Zhang, Y. Z. Dong and Y. B. Sheng J. Chem. Phys. 143, 134101 (2014). Crossref, Web of Science, ADS, Google Scholar
32. E. Agliari, Phys. Rev. E 77, 011128 (2008). Crossref, Web of Science, ADS, Google Scholar
33. V. Balakrishnan, E. Abad, T. Abil and J. J. Kozak, Phys. Rev. E 99, 062110 (2019). Crossref, Web of Science, ADS, Google Scholar
34. E. A. Codling, M. J. Plank and S. Benhamou, J. R. Soc. Interface 5, 813 (2008). Crossref, Web of Science, Google Scholar
35. K. Ishihara, A. B. George, R. Cornelius and K. S. Korolev, New J. Phys. 22, 083034 (2020). Crossref, Web of Science, Google Scholar
36. G. M. Schütz and S. Trimper, Phys. Rev. E 70, 045101 (2004). Crossref, Web of Science, ADS, Google Scholar
37. C. F. Coletti and I. Papageorgiou, J. Stat. Mech. 1, 013205 (2021). Crossref, Web of Science, Google Scholar
38. J. Peng, E. Agliari and Z. Zhang, Chaos 7, 073118 (2015). Crossref, Web of Science, Google Scholar
39. Z. Z. Zhang, H. Li and Y. H. Yi, J. Chem. Phys. 143, 064901 (2015). Crossref, Web of Science, Google Scholar
40. Z. Z. Zhang, Y. Z. Dong and Y. B. Sheng, J. Chem. Phys. 143, 134101 (2015). Crossref, Web of Science, ADS, Google Scholar
41. B. Wu et al., J. Stat. Mech. 10, 103207 (2019). Crossref, Web of Science, Google Scholar
42. Y. Gao and Z. K. Wu, Int. J. Mod. Phys. B 32, 1850224 (2018). Link, Web of Science, ADS, Google Scholar
43. G. Y. Xu and Z. K. Wu, IEEE Access 8, 138058 (2020). Crossref, Web of Science, Google Scholar