Impact of the heterogeneity of adoption thresholds on behavior spreading in complex networks. (English) Zbl 1461.91233
Summary: Individuals always exhibit distinct personal profiles ranging from education, social experiences to risk tolerance, which induces a vastly different response in the behavior spreading dynamics. To describe this phenomenon, a widely used method is to assign a distinct adoption threshold for each individual, which so far has eluded theoretical analysis. In this paper, we propose a behavior spreading model to describe the heterogeneity of individuals in adopting the behavior, in which the adoption threshold follows the Gaussian distribution. Based on the edge-based compartmental theory, the theoretical solutions of the behavior spreading size and the threshold are given for discontinuous and continuous phase transitions. Through theoretical analysis and extensive numerical simulations, the impact of the heterogeneity of adoption thresholds on behavior spreading is demonstrated, and we find that the phase transition depends on the mean and standard deviation of the adoption thresholds. For small values of the mean adoption threshold, the system exhibits a continuous phase transition. For large values of the mean adoption threshold, the phase transition is discontinuous (continuous) for the small (large) standard deviation of the adoption thresholds. There is a remarkable agreement between theoretical predictions and numerical simulations.
MSC:
| 91D30 | Social networks; opinion dynamics |
References:
| [1] | Pastor-Satorras, R.; Castellano, C.; Mieghem, P. V.; Vespignani, A., Epidemic processes in complex networks, Review of Modern Physics, 87, 3, 925-979 (2015) |
| [2] | Wang, Z.; Moreno, Y.; Boccaletti, S.; Perc, M., Vaccination and epidemics in networked populations an introduction, Chaos, Solitons & Fractals, 103, 177-183 (2017) |
| [3] | Dodds, P. S.; Watts, D. J., Universal behavior in a generalized model of contagion, Phys. Rev. Lett., 92, 218701 (2004) |
| [4] | Yagan, O.; Gligor, V., Analysis of complex contagions in random multiplex networks, Phys. Rev. E, 86, 036103 (2012) |
| [5] | Gleeson, J. P., Binary-state dynamics on complex networks: pair approximation and beyond, Phys. Rev. X, 3, 021004 (2013) |
| [6] | Melnik, S.; Ward, J.; Gleeson, J.; Porter, M., Multi-stage complex contagions, Chaos, 23, 013124 (2013) |
| [7] | Wang, X.; Jia, D.; Gao, S.; Xia, C.; Li, X.; Wang, Z., Vaccination behavior by coupling the epidemic spreading with the human decision under the game theory, Applied Mathematics and Computation, 380, 125232 (2020) · Zbl 1460.92122 |
| [8] | Chang, H. H.; Fu, F., Co-diffusion of social contagions, New Journal of Physics, 20, 9, 095001 (2018) |
| [9] | Hoffmann, X.; Boguñá, M., Memory-induced complex contagion in epidemic spreading, New Journal of Physics, 21, 3, 033034 (2019) |
| [10] | Cencetti, G.; Battiston, F., Diffusive behavior of multiplex networks, New Journal of Physics, 21, 3, 035006 (2019) |
| [11] | Ma, C.; Chen, H.; Li, X.; Lai, Y., Data based reconstruction of duplex networks, SIAM Journal on Applied Dynamical Systems, 19, 124-150 (2020) · Zbl 1437.37123 |
| [12] | Li, S.; Zhao, D.; Wu, X.; Tian, Z.; Li, A.; Wang, Z., Functional immunization of networks based on message passing, Applied Mathematics and Computation, 366, 124728 (2020) · Zbl 1433.91115 |
| [13] | Perc, M., Diffusion dynamics and information spreading in multilayer networks: An overview, European Physical Journal: Special Topics, 228, 11, 2351-2355 (2019) |
| [14] | Kan, J.; Zhang, H., Effects of awareness diffusion and self-initiated awareness behavior on epidemic spreading - an approach based on multiplex networks, Communications in Nonlinear Science and Numerical Simulation, 44, 193-203 (2017) · Zbl 1466.92189 |
| [15] | Zhang, H.; Wang, Z., Suppressing epidemic spreading by imitating hub nodes strategy, IEEE Transactions on Circuits and Systems II: Express Briefs, 1 (2019) |
| [16] | Christakis, N. A.; Fowler, J. H., The spread of obesity in a large social network over 32 years, New England Journal of Medicine, 357, 4, 370-379 (2007) |
| [17] | Moreno, Y.; Nekovee, M.; Pacheco, A. F., Dynamics of rumor spreading in complex networks, Phys. Rev. E, 69, 6, 066130 (2004) |
| [18] | Borge-Holthoefer, J.; Moreno, Y., Absence of influential spreaders in rumor dynamics, Phys. Rev. E, 85, 026116 (2012) |
| [19] | Wang, J.; Zhao, L.; Huang, R., Siraru rumor spreading model in complex networks, Physica A: Statistical Mechanics & Its Applications, 398, 43-55 (2014) · Zbl 1402.91608 |
| [20] | Li, W.; Tang, S.; Pei, S.; Yan, S.; Jiang, S.; Teng, X.; Zheng, Z., The rumor diffusion process with emerging independent spreaders in complex networks, Physica A: Statistical Mechanics & Its Applications, 397, 121-128 (2014) · Zbl 1402.91633 |
| [21] | Gao, L.; Wang, W.; Pan, L.; Tang, M.; Zhang, H., Effective information spreading based on local information in correlated networks, Sci Rep, 6, 38220 (2016) |
| [22] | Zhang, Z.; Liu, C.; Zhan, X.; Lu, X.; Zhang, C.; Zhang, Y., Dynamics of information diffusion and its applications on complex networks, Physics Reports, 651, 1-34 (2016) |
| [23] | Liu, X.; Liu, C.; Zeng, X., Online social network emergency public event information propagation and nonlinear mathematical modeling, Complexity 2017, 1-7 (2017) · Zbl 1407.91202 |
| [24] | Centola, D., The spread of behavior in an online social network experiment, Science, 329, 5996, 1194-1197 (2010) |
| [25] | Centola, D., An experimental study of homophily in the adoption of health behavior, Science, 334, 6060, 1269-1272 (2011) |
| [26] | Karsai, M.; Iñiguez, G.; Kikas, R.; Kaski, K.; Kertész, J., Local cascades induced global contagion: How heterogeneous thresholds, exogenous effects, and unconcerned behaviour govern online adoption spreading, Scientific Reports, 6, 27178 (2016) |
| [27] | Young, H. P., The dynamics of social innovation, Proc Natl Acad Sci U S A, 108, Suppl 4, 21285-21291 (2011) |
| [28] | Banerjee, A.; Chandrasekhar, A. G.; Duflo, E.; Jackson, M. O., The diffusion of microfinance, Science, 341, 6144, 1236498 (2013) |
| [29] | Liu, C.; Zhan, X.; Zhang, Z.; Sun, G.; Hui, P. M., How events determine spreading patterns: information transmission via internal and external influences on social networks, New Journal of Physics, 17, 11, 113045 (2015) |
| [30] | Liu, C.; Zhou, N.; Zhan, X.; Sun, G.; Zhang, Z., Markov-based solution for information diffusion on adaptive social networks, Applied Mathematics and Computation, 380, 125286 (2020) · Zbl 1460.91196 |
| [31] | Zhan, X.; Liu, C.; Zhou, G.; Zhang, Z.; Sun, G.; Zhu, J.; Jin, Z., Coupling dynamics of epidemic spreading and information diffusion on complex networks, Applied Mathematics and Computation, 332, 437-448 (2018) · Zbl 1427.92097 |
| [32] | Watts, D., A simple model of global cascades on random networks, Proceedings of the National Academy of Sciences of the United States of America, 99, 9, 5766-5771 (2002) · Zbl 1022.90001 |
| [33] | Granovetter, M. S., The strength of weak ties, American Journal of Sociology, 78, 6, 1360-1380 (1973) |
| [34] | Wang, W.; Tang, M.; Zhang, H.; Lai, Y., Dynamics of social contagions with memory of nonredundant information, Phys. Rev. E, 92, 1, 012820 (2015) |
| [35] | Unicomb, S.; Iñiguez, G.; Karsai, M., Threshold driven contagion on weighted networks, Scientific Reports, 8, 1 (2017) |
| [36] | Backlund, V.-P.; Saramaki, J.; Pan, R. K., Effects of temporal correlations on cascades: Threshold models on temporal networks, Phys.Rev. E, 89, 6, 062815 (2014) |
| [37] | Liu, M.; Wang, W.; Liu, Y.; Tang, M.; Cai, S.; Zhang, H., Social contagions on time-varying community networks, Phys.Rev.E, 95, 5, 052306 (2017) |
| [38] | 1-088701.5 |
| [39] | Wang, W.; Cai, M.; Zheng, M., Social contagions on correlated multiplex networks, Physica A: Statistical Mechanics & its Applications, 499, 121-128 (2017) · Zbl 1514.91158 |
| [40] | Chatterjee, S.; Durrett, R., Contact processes on random graphs with power law degree distributions have critical value 0, Ann. Probab, 37, 6 (2009) · Zbl 1205.60168 |
| [41] | Wang, W.; Tang, M.; Shu, P.; Wang, Z., Dynamics of social contagions with heterogeneous adoption thresholds: crossover phenomena in phase transition, New Journal of Physics, 18, 1, 013029 (2016) · Zbl 1456.91105 |
| [42] | Karampourniotis, P. D.; Sreenivasan, S.; Szymanski, B. K.; Korniss, G., The impact of heterogeneous thresholds on social contagion with multiple initiators, Plos One, 10, 11, e0143020 (2015) |
| [43] | Zhu, X.; Tian, H.; Chen, X.; Wang, W.; Cai, S., Heterogeneous behavioral adoption in multiplex networks, New Journal of Physics, 20, 12, 125002 (2018) |
| [44] | Karrer, B.; Newman, M. E.J., Message passing approach for general epidemic models, Phys. Rev. E, 82, 1, 016101 (2010) |
| [45] | Karrer, B.; Newman, M. E.J.; Zdeborová, L., Percolation on sparse networks, Phys. Rev. Lett, 113, 20, 208702 (2014) |
| [46] | Shafer, D., Nonlinear dynamics and chaos: With applications to physics, biology, chemistry, and engineering (steven h. strogatz), Siam Review, 37, 2 (1995) |
| [47] | Newman, M. E.J., Spread of epidemic disease on networks, Phys. Rev. E, 66, 016128 (2002) |
| [48] | Aludaat, K.; Alodat, M., A note on approximating the normal distribution function, Applied Mathematical Sciences (Ruse), 2, 9, 425-429 (2008) · Zbl 1151.62307 |
| [49] | Erdos, P.; Rényi, A., On random graphs i, Publ. Math. Debrecen, 6, 290-297 (1959) · Zbl 0092.15705 |
| [50] | Catanzaro, M.; Boguñá, M.; Pastor-Satorras, R., Generation of uncorrelated random scale-free networks, Phys. Rev. E, 71, 2, 027103 (2005) |
| [51] | Schroder, M.; D’Souza, R.; Sornette, D.; Nagler, J., Microtransition cascades to percolation, Phys. Rev. Lett., 112, 15, 155701 (2014) |
| [52] | Gao, L.; Li, R.; Shu, P.; Wang, W.; Gao, H.; Cai, S., Effects of individual popularity on information spreading in complex networks, Physica A: Statistical Mechanics and its Applications, 489, 32-39 (2018) · Zbl 1514.91141 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
