Effects of heterogeneous adoption thresholds on contact-limited social contagions
Dan-Dan Zhao(赵丹丹)1, Wang-Xin Peng(彭王鑫)2, Hao Peng(彭浩)1,3, and Wei Wang(王伟)4,†
1 College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, China; 2 College of Information, Zhejiang Guangsha Vocational and Technical University of Construction, Dongyang 322100, China; 3 Shanghai Key Laboratory of Integrated Administration Technologies for Information Security, Shanghai 200240, China; 4 School of Public Health and Management, Chongqing Medical University, Chongqing 400016, China
Abstract Limited contact capacity and heterogeneous adoption thresholds have been proven to be two essential characteristics of individuals in natural complex social systems, and their impacts on social contagions exhibit complex nature. With this in mind, a heterogeneous contact-limited threshold model is proposed, which adopts one of four threshold distributions, namely Gaussian distribution, log-normal distribution, exponential distribution and power-law distribution. The heterogeneous edge-based compartmental theory is developed for theoretical analysis, and the calculation methods of the final adoption size and outbreak threshold are given theoretically. Many numerical simulations are performed on the Erdös-Rényi and scale-free networks to study the impact of different forms of the threshold distribution on hierarchical spreading process, the final adoption size, the outbreak threshold and the phase transition in contact-limited propagation networks. We find that the spreading process of social contagions is divided into three distinct stages. Moreover, different threshold distributions cause different spreading processes, especially for some threshold distributions, there is a change from a discontinuous first-order phase transition to a continuous second-order phase transition. Further, we find that changing the standard deviation of different threshold distributions will cause the final adoption size and outbreak threshold to change, and finally tend to be stable with the increase of standard deviation.
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 62072412, 61902359, 61672467, and 61672468), the Social Development Project of Zhejiang Provincial Public Technology Research (Grant No. 2016C33168), Zhejiang Provincial Natural Science Foundation of China (Grant No. LQ19F030010), and the Opening Project of Shanghai Key Laboratory of Integrated Administration Technologies for Information Security (Grant No. AGK2018001).
Corresponding Authors:
Wei Wang
E-mail: wwzqbc@cqmu.edu.cn,wwzqbx@hotmail.com
Cite this article:
Dan-Dan Zhao(赵丹丹), Wang-Xin Peng(彭王鑫), Hao Peng(彭浩), and Wei Wang(王伟) Effects of heterogeneous adoption thresholds on contact-limited social contagions 2022 Chin. Phys. B 31 068906
[1] Jeong H M, Mason S P, Barabási A and Oltvai Z N 2001 Nature411 41 [2] Dunne J A, Williams R J and Martinez N D 2002 Proc. Natl. Acad. Sci. USA99 12917 [3] Motter A E, Myers S A, Anghel M and Nishikawa T 2013 Nat. Phys.9 191 [4] Faloutsos M, Faloutsos P and Faloutsos C 1999 ACM SIGCOMM Comput. Commun. Rev.29 251 [5] Ebel H, Mielsch L I and Bornholdt S 2002 Phys. Rev. E66 035103 [6] Serrano M A and Bogu ná M 2003 Phys. Rev. E68 015101 [7] Yang Y Z, Hu M and Huang T Y 2020 Chin. Phys. B29 088903 [8] Wang W, Li W Y, Lin T, Wu T, Pan L M and Liu Y B 2021 Appl. Math. Comput. 126793 (In Press) [9] Pan L M, Wang W, Tian L and Lai Y C 2021 Phys. Rev. E103 012302 [10] Watts D J and Strogatz S H 1998 Nature393 440 [11] Albert R and Barabási A L 2002 Rev. Mod. Phys.74 47 [12] Newman M E J 2003 SIAM Rev.45 167 [13] Boccaletti S, Bianconi G, Criado R, del Genio C I, Gómez-Gardeñes J, Romance M, Sendiña-Nadal I, Wang Z and Zanin M 2014 Phys. Rep.544 1 [14] Hawoong Jeong R A and Barabási A 2000 Nature406 378 [15] Callaway D S, Newman M E J, Strogatz S H and Watts D J 2000 Phys. Rev. Lett.85 5468 [16] Cohen R, Erez K, ben-Avraham D and Havlin S 2000 Phys. Rev. Lett.85 4626 [17] Song C, Havlin S and Makse H A 2005 Nature433 392 [18] Arenas A, Diaz-Guilera A, Kurths J, Moreno Y and Zhou C 2008 Phys. Rep.469 93 [19] Radicchi F 2015 Nat. Phys.11 597 [20] Li D Q, Fu B W, Wang Y P, Lu G Q, Berezin Y, Stanley H E and Havlin S 2015 Proc. Natl. Acad. Sci. USA112 669 [21] Zhang M, Wang X J, Jin L, Song M and Liao Z H 2020 Chin. Phys. B29 096401 [22] Liu J 2021 Chin. Phys. B30 016401 [23] Li W Y, Xue X, Pan L M, Lin T and Wang W 2022 Appl. Math. Comput.412 126595 [24] Saumell-Mendiola A, Serrano M A and Boguná M 2012 Phys. Rev. E86 026106 [25] Sun Y, Liu C, Zhang C X and Zhang Z K 2014 Phys. Lett. A378 635 [26] Gosak M, Duh M, Markovi R and Perc M 2021 New J. Phys.23 043039 [27] Brett T, Loukas G, Moreno Y and Perra N 2019 Phys. Rev. E99 050303 [28] Okamoto T and Ishida Y 2002 Syst. Comput. Jpn.33 81 [29] Feng Y, Ding L, Huang Y H and Guan Z H 2016 Chin. Phys. B25 128903 [30] Lu Y L, Jiang G P and Song Y R 2012 Chin. Phys. B21 100207 [31] Zan Y 2018 Chaos, Solitons & Fractals110 191 [32] Cheng Y, Huo L and Zhao L 2021 Inf. Sci.564 237 [33] Liu W, Wu X, Yang W, Zhu X and Zhong S 2019 Appl. Math. Comput.343 214 [34] Chen N, Zhu X and Chen Y 2019 Physica A523 671 [35] Zhang Y, Su Y, Li W and Liu H 2019 Chaos, Solitons & Fractals121 168 [36] Gao X and Tian L 2019 Physica A514 226 [37] Karsai M, Iniguez G, Kaski K and Kertesz J 2014 J. R. Soc. Interface11 20140694 [38] Ma Y, Xue X, Cai M and Wang W 2020 Chin. Phys. B29 128902 [39] Zhan X X, Liu C, Zhou G, Zhang Z K, Sun G Q, Zhu J and Jin Z 2018 Appl. Math. Comput.332 437 [40] Guo H, Wang Z, Sun S and Xia C 2021 Phys. Lett. A398 127282 [41] Zhu L, Liu W and Zhang Z 2021 Math. Comput. Simul.188 268 [42] Wang W, Liu Q H, Liang J, Hu Y and Zhou T 2019 Phys. Rep.820 1 [43] Peng X L and Zhang Y D 2021 Chin. Phys. B30 058901 [44] Granovetter M S 1973 Am. J. Sociol.78 1360 [45] Watts D J 2002 Proc. Natl. Acad. Sci. USA99 5766 [46] Wang W, Tang M, Zhang H F and Lai Y C 2015 Phys. Rev. E92 012820 [47] Wang W, Tang M, Shu P and Wang Z 2016 New J. Phys.18 013029 [48] Wang X, Lan Y and Xiao J 2019 Physica A531 121721 [49] Backlund V P, Saramaki J and Pan R K 2014 Phys. Rev. E89 062815 [50] Unicomb S, I niguez G and Karsai M 2018 Sci. Rep.8 3094 [51] Han L L, Lin Z H, Tang M, Zhou J, Zou Y and Guan S G 2020 Phys. Rev. E101 042308 [52] Zhu X, Tian H, Chen X, Wang W and Cai S 2018 New J. Phys.20 125002 [53] Karampourniotis P D, Sameet S, Szymanski B K, Gyorgy K and Adriana B L 2015 PLoS One10 e0143020 [54] Peng H, Peng W X, Zhao D D and Wang W 2020 Appl. Math. Comput.386 125504 [55] Ren J, Yang Q, Zhu Y, Zhu X and Cai S 2020 IEEE Acc.8 61905 [56] Bao P, Shen H W and Cheng X Q 2013 PlOS one8 e76027 [57] Yang Z, Cui A X and Zhou T 2011 Physica A390 4543 [58] Chatterjee S and Durrett R 2009 Ann. Probab.37 2332 [59] Xiong F, Zheng Y, Wang H, Wang X and Chen H 2021 Future Generation Computer Systems114 307 [60] Jiang J and Zhou T 2018 Physica A508 414 [61] Tian G and Wang Z C 2020 Appl. Math. Lett.102 106121 [62] Wang W, Shu P P, Zhu Y X, Tang M and Zhang Y C 2015 Chaos25 103102 [63] Zhu Y X, Cao Y Y, Chen T, Qiu X Y, Wang W and Hou R 2018 Chaos Solitons & Fractals114 408 [64] Karrer B and Newman M E J 2010 Phys. Rev. E82 016101 [65] Karrer B, Newman M E J and Zdeborová L 2014 Phys. Rev. Lett.113 208702 [66] Erdös P and Rényi A 1959 Publ. Math. Debrecen6 290 [67] Catanzaro M, Bogu ná M and Pastor-Satorras R 2005 Phys. Rev. E71 027103 [68] Lou J 2007 Ecology88 2427 [69] Chen W, Schroder M, D'Souza R M, Sornette D and Nagler J 2014 Phys. Rev. Lett.112 155701
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
