Skip to main content
Log in

Recent advances in opinion propagation dynamics: a 2020 survey

  • Review
  • Published:
The European Physical Journal Plus Aims and scope Submit manuscript

Abstract

Opinion dynamics have attracted the interest of researchers from different fields. Local interactions among individuals create interesting dynamics for the system as a whole. Such dynamics are important from a variety of perspectives. Group decision making, successful marketing, and constructing networks (in which consensus can be reached or prevented) are a few examples of existing or potential applications. The invention of the Internet has made the opinion fusion faster, unilateral, and on a whole different scale. Spread of fake news, propaganda, and election interferences have made it clear there is an essential need to know more about these dynamics. The emergence of new ideas in the field has accelerated over the last few years. In the first quarter of 2020, at least 50 research papers have emerged, either peer-reviewed and published or on preprint outlets such as arXiv. In this paper, we summarize these ground-breaking ideas and their fascinating extensions and introduce newly surfaced concepts.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2

Similar content being viewed by others

References

  1. J.R.P. French Jr., A formal theory of social power. Psychol. Rev. 63(3), 181–194 (1956)

    Google Scholar 

  2. M. DeGroot, Reaching a consensus. J. Am. Stat. Assoc. 69(345), 118–121 (1974)

    MATH  Google Scholar 

  3. S. Biswas, P. Sen, Model of binary opinion dynamics: coarsening and effect of disorder. Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 80(2), 4–7 (2009)

    Google Scholar 

  4. F. Ding, Y. Liu, B. Shen, X.-M. Si, An evolutionary game theory model of binary opinion formation. Physica A 389(8), 1745–1752 (2010)

    ADS  Google Scholar 

  5. A. Mukhopadhyay, R.R. Mazumdar, R. Roy, Opinion dynamics under voter and majority rule models with biased and stubborn agents. arXiv:2003.02885 (2020)

  6. G. Deffuant, D. Neau, F. Amblard, G. Weisbuch, Mixing beliefs among interacting agents. Adv. Complex Syst. 03(01n04), 87–98 (2000)

    Google Scholar 

  7. H. Noorazar, M.J. Sottile, K.R. Vixie, An energy-based interaction model for population opinion dynamics with topic coupling. Int. J. Mod. Phys. C 29(11), 1850115 (2018)

    ADS  Google Scholar 

  8. A.C.R. Martins, Continuous opinions and discrete actions in opinion dynamics problems. Int. J. Mod. Phys. C 19(4), 617–624 (2007)

    ADS  MATH  Google Scholar 

  9. A.C.R. Martins, Discrete opinion dynamics with M choices. Eur. Phys. J. B 93(1), 1 (2020)

    ADS  MathSciNet  Google Scholar 

  10. Y. Yi, S. Patterson, Disagreement and polarization in two-party social networks. arXiv:1911.11338 (2019)

  11. H.Z. Brooks, M.A. Porter, A model for the influence of media on the ideology of content in online social networks. Phys. Rev. Res. 2, 023041 (2020)

    Google Scholar 

  12. O. Abrahamsson, D. Danev, E.G. Larsson, Opinion dynamics with random actions and a stubborn agent. arXiv:1912.04183 (2019)

  13. F. Jacobs, S. Galam, Two-opinions-dynamics generated by inflexibles and non-contrarian and contrarian floaters. Adv. Complex Syst. 22(04), 1950008 (2019)

    MathSciNet  Google Scholar 

  14. S. Galam, F. Jacobs, The role of inflexible minorities in the breaking of democratic opinion dynamics. Physica A 381, 366–376 (2007)

    ADS  Google Scholar 

  15. B. Chazelle, C. Wang, Inertial Hegselmann–Krause systems. IEEE Trans. Autom. Control 62(8), 3905–3913 (2017)

    MathSciNet  MATH  Google Scholar 

  16. J. Lorenz, Heterogeneous bounds of confidence: meet, discuss and find consensus!. Complexity 15(4), 43–52 (2010)

    MathSciNet  Google Scholar 

  17. R.L. Berger, A necessary and sufficient condition for reaching a consensus using Degroot’s method. J. Am. Stat. Assoc. 76(374), 415–418 (1981)

    MathSciNet  MATH  Google Scholar 

  18. N. Friedkin, E. Johnsen, Social influence and opinions. J. Math. Sociol. 15, 193–206 (1990)

    MATH  Google Scholar 

  19. N. Friedkin, E. Johnsen, Social influence networks and opinion change models of opinion formation. Adv. Group Process. 16, 1–29 (1999)

    Google Scholar 

  20. S.E. Parsegov, A.V. Proskurnikov, R. Tempo, N.E. Friedkin, Novel multidimensional models of opinion dynamics in social networks. IEEE Trans. Autom. Control 62(5), 2270–2285 (2017)

    MathSciNet  MATH  Google Scholar 

  21. R. Hegselmann, U. Krause, Opinion dynamics and bounded confidence: models, analysis and simulation. J. Artif. Soc. Soc. Simul. 5(3), 1–30 (2002)

    Google Scholar 

  22. P. Sobkowicz, Extremism without extremists: Deffuant model with emotions. Front. Phys. 3, 17 (2015)

    Google Scholar 

  23. S. Fortunato et al., Universality of the threshold for complete consensus for the opinion dynamics of Deffuant. Int. J. Mod. Phys. C 15(09), 1301–1307 (2004)

    ADS  Google Scholar 

  24. C. Castellano, S. Fortunato, V. Loreto, Statistical physics of social dynamics. Rev. Mod. Phys. 81(2), 591 (2009)

    ADS  Google Scholar 

  25. G. Chen, W. Su, W. Mei, F. Bullo, Convergence properties of the heterogeneous Deffuant–Weisbuch model. arXiv:1901.02092 (2019)

  26. J. Zhang, G. Chen, Convergence rate of the asymmetric Deffuant–Weisbuch dynamics. J. Syst. Sci. Complex. 28(4), 773–787 (2015)

    MathSciNet  MATH  Google Scholar 

  27. Y. Shang, An agent based model for opinion dynamics with random confidence threshold. Commun. Nonlinear Sci. Numer. Simul. 19(10), 3766–3777 (2014)

    ADS  MathSciNet  MATH  Google Scholar 

  28. C. Huang, Q. Dai, W. Han, Y. Feng, H. Cheng, H. Li, Effects of heterogeneous convergence rate on consensus in opinion dynamics. Physica A 499, 428–435 (2018)

    ADS  Google Scholar 

  29. A. Bhattacharyya, M. Braverman, B. Chazelle, H.L. Nguyen, On the convergence of the Hegselmann–Krause system, in Proceedings of the 4th Conference on Innovations in Theoretical Computer Science, ITCS ’13 (Association for Computing Machinery, New York, NY, USA, 2013), pp. 61–66

  30. D. Stauffer, A.O. Sousa, C. Schulze, Discretized opinion dynamics of Deffuant on scale-free networks. J. Artif. Soc. Soc. Simul. 7(3), 21 (2003)

    Google Scholar 

  31. S. Galam, The Trump phenomenon: an explanation from sociophysics. Int. J. Mod. Phys. B 31(10), 1742015 (2017)

    ADS  MathSciNet  Google Scholar 

  32. S. Biswas, P. Sen, Critical noise can make the minority candidate win: the US presidential election cases. Phys. Rev. E 96(3), 032303 (2017)

    ADS  Google Scholar 

  33. N.E. Friedkin, A formal theory of social power. J. Math. Sociol. 12(2), 103–126 (1986)

    ADS  MATH  Google Scholar 

  34. S. Galam, Y. Gefen, Y. Shapir, Sociophysics: a new approach of sociological collective behaviour. I. Mean-behaviour description of a strike. J. Math. Sociol. 9(1), 1–13 (1982)

    MATH  Google Scholar 

  35. S. Galam, Majority rule, hierarchical structures, and democratic totalitarianism: a statistical approach. J. Math. Psychol. 30(4), 426–434 (1986)

    MATH  Google Scholar 

  36. S. Galam, Sociophysics: a review of galam models. Int. J. Mod. Phys. C 19(03), 409–440 (2008)

    ADS  MATH  Google Scholar 

  37. S. Galam, Sociophysics, A Physicist’s Modeling of Psycho-political Phenomena (Springer, New York, 2012)

    Google Scholar 

  38. B. Gärtner, A.N. Zehmakan, Threshold behavior of democratic opinion dynamics. J. Stat. Phys. 178, 1442–1466 (2020)

    ADS  MathSciNet  MATH  Google Scholar 

  39. K. Sznajd-Weron, J. Sznajd, Opinion evolution in closed community. Int. J. Mod. Phys. C 11(06), 1157–1165 (2000)

    ADS  MATH  Google Scholar 

  40. F. Slanina, H. Lavicka, Analytical results for the Sznajd model of opinion formation. Eur. Phys. J. B Condens. Matter Complex Syst. 35(2), 279–288 (2003)

    Google Scholar 

  41. R. Muslim, R. Anugraha, S. Sholihun, M.F. Rosyid, Phase transition of the Sznajd model with anticonformity for two different agent configurations. Int. J. Mod. Phys. C 0(0), 2050052 (2020)

    MathSciNet  Google Scholar 

  42. M. Calvelli, N. Crokidakis, T.J.P. Penna, Phase transitions and universality in the Sznajd model with anticonformity. Physica A 513, 518–523 (2019)

    ADS  MathSciNet  Google Scholar 

  43. K. Sznajd-Weron, Sznajd model and its applications. arXiv:physics/0503239v1 (2005)

  44. D. Stauffer, Sociophysics: the Sznajd model and its applications. Comput. Phys. Commun. 146(1), 93–98 (2002). Proceedings of the STATPHYS Satellite Conference: Challenges in Computational Statistical Physics in teh 21st CenturyProceedings of the STATPHYS Satellite Conference: Challenges in Computational Statistical Physics in teh 21st Century

    ADS  MATH  Google Scholar 

  45. V. Sood, S. Redner, Voter model on heterogeneous graphs. Phys. Rev. Lett. 94(17), 178701 (2005)

    ADS  Google Scholar 

  46. M.T. Gastner, K. Ishida, Voter model on networks partitioned into two cliques of arbitrary sizes. J. Phys. A: Math. Theor. 52(50), 505701 (2019)

    MathSciNet  Google Scholar 

  47. J.R. Majmudar, S.M. Krone, B.O. Baumgaertner, R.C. Tyson, Voter models and external influence. J. Math. Sociol. 44(1), 1–11 (2020)

    MathSciNet  Google Scholar 

  48. I. Caridi, S. Manterola, V. Semeshenko, P. Balenzuela, Topological study of the convergence in the voter model. Appl. Netw. Sci. 4(1), 1–13 (2019)

    Google Scholar 

  49. S. Redner, Reality-inspired voter models: a mini-review. C. R. Phys. 20(4), 275–292 (2019)

    ADS  MathSciNet  Google Scholar 

  50. H. Wai, A. Scaglione, A. Leshem, Active sensing of social networks. IEEE Trans. Signal Inf. Process. Netw. 2(3), 406–419 (2016)

    MathSciNet  Google Scholar 

  51. Q. Zhou, W. Zhibin, A.H. Altalhi, F. Herrera, A two-step communication opinion dynamics model with self-persistence and influence index for social networks based on the Degroot model. Inf. Sci. 519, 363–381 (2020)

    MathSciNet  Google Scholar 

  52. S. Huang, B. Xiu, Y. Feng, Modeling and simulation research on propagation of public opinion, in 2016 IEEE Advanced Information Management, Communicates, Electronic and Automation Control Conference (IMCEC) (IEEE, 2016), pp. 380–384

  53. T. Cheon, S. Galam, Dynamical galam model. Phys. Lett. A 382(23), 1509–1515 (2018)

    ADS  MathSciNet  MATH  Google Scholar 

  54. S. Galam, T. Cheon, Tipping point dynamics: a universal formula. arXiv:1901.09622 (2019)

  55. S. Qian, Y. Liu, S. Galam, Activeness as a key to counter democratic balance. Physica A 432, 187–196 (2015)

    ADS  MathSciNet  MATH  Google Scholar 

  56. T. Cheon, J. Morimoto, Balancer effects in opinion dynamics. Phys. Lett. A 380(3), 429–434 (2016)

    ADS  Google Scholar 

  57. S. Galam, T. Cheon, Asymmetric contrarians in opinion dynamics. Entropy 22(1), 25 (2020)

    ADS  MathSciNet  Google Scholar 

  58. M. Mobilia, A. Petersen, S. Redner, On the role of zealotry in the voter model. J. Stat. Mech. Theory Exp. 2007(08), P08029–P08029 (2007)

    MathSciNet  MATH  Google Scholar 

  59. N. Khalil, M. San Miguel, R. Toral, Zealots in the mean-field noisy voter model. Phys. Rev. E 97, 012310 (2018)

    ADS  Google Scholar 

  60. E. Yildiz, A. Ozdaglar, D. Acemoglu, A. Saberi, A. Scaglione, Binary opinion dynamics with stubborn agents. ACM Trans. Econ. Comput. 1(4), 1–30 (2013)

    Google Scholar 

  61. P. Dandekar, A. Goel, D.T. Lee, Biased assimilation, homophily, and the dynamics of polarization. Proc. Natl. Acad. Sci. 110(15), 5791–5796 (2013)

    ADS  MathSciNet  MATH  Google Scholar 

  62. W. Xia, M. Ye, J. Liu, M. Cao, X.-M. Sun, Analysis of a nonlinear opinion dynamics model with biased assimilation. arXiv:1912.01778 (2019)

  63. A. Sîrbu, D. Pedreschi, F. Giannotti, J. Kertész, Algorithmic bias amplifies opinion fragmentation and polarization: a bounded confidence model. PLoS ONE 14(3), e0213246 (2019)

    Google Scholar 

  64. X. Chen, X. Zhang, Y. Xie, W. Li, Opinion dynamics of social-similarity-based Hegselmann–Krause model. Complexity 2017, 1820257 (2017)

    MATH  Google Scholar 

  65. F. Guiyuan, W. Zhang, Z. Li, Opinion dynamics of modified Hegselmann–Krause model in a group-based population with heterogeneous bounded confidence. Physica A 419, 558–565 (2015)

    ADS  MATH  Google Scholar 

  66. Y. Dong, Z. Ding, L. Martínez, F. Herrera, Managing consensus based on leadership in opinion dynamics. Inf. Sci. 397–398, 187–205 (2017)

    MATH  Google Scholar 

  67. M. Pineda, G.M. Buendía, Mass media and heterogeneous bounds of confidence in continuous opinion dynamics. Physica A 420, 73–84 (2015)

    ADS  MathSciNet  MATH  Google Scholar 

  68. D. Bauso, M. Cannon, Consensus in opinion dynamics as a repeated game. Automatica 90, 204–211 (2018)

    MathSciNet  MATH  Google Scholar 

  69. R. Hegselmann, S. König, S. Kurz, C. Niemann, J. Rambau, Optimal opinion control: the campaign problem. arXiv preprint arXiv:1410.8419 (2014)

  70. J. Gaitonde, J. Kleinberg, E. Tardos, Adversarial perturbations of opinion dynamics in networks. arXiv:2003.07010 (2020)

  71. T. Carletti, D. Fanelli, S. Grolli, A. Guarino, How to make an efficient propaganda. Europhys. Lett. 74(2), 222–228 (2006)

    ADS  Google Scholar 

  72. R. Hegselmann, U. Krause, Opinion dynamics under the influence of radical groups, charismatic leaders, and other constant signals: a simple unifying model. Netwo. Heterog. Media 10(3), 477–509 (2015)

    MathSciNet  MATH  Google Scholar 

  73. A. Gupta, S. Moharir, N. Sahasrabudhe, Influencing opinion dynamics in networks with limited interaction. arXiv:2002.00664 (2020)

  74. G. Romero Moreno, E. Manino, L. Tran-Thanh, M. Brede, Zealotry and influence maximization in the voter model: when to target partial zealots?, in Complex Networks XI, ed. by H. Barbosa, J. Gomez-Gardenes, B. Gonçalves, G. Mangioni, R. Menezes, M. Oliveira (Springer, Cham, 2020), pp. 107–118

    Google Scholar 

  75. Q. He, X. Wang, B. Yi, F. Mao, Y. Cai, M. Huang, Opinion maximization through unknown influence power in social networks under weighted voter model. IEEE Syst. J. 14, 1–12 (2019)

    Google Scholar 

  76. R. Hegselmann, S. König, S. Kurz, C. Niemann, J. Rambau, Optimal opinion control: the campaign problem. Jasss 18(3), 1–40 (2015)

    Google Scholar 

  77. I.C. Morărescu, V.S. Varma, L. Buşoniu, S. Lasaulce, Space-time budget allocation policy design for viral marketing. Nonlinear Anal. Hybrid Syst. 37, 100899 (2020)

    MathSciNet  Google Scholar 

  78. F. Dietrich, S. Martin, M. Jungers, Control via leadership of opinion dynamics with state and time-dependent interactions. IEEE Trans. Autom. Control 63(4), 1200–1207 (2018)

    MathSciNet  MATH  Google Scholar 

  79. M. Goyal, D. Manjunath, Opinion control competition in a social network. In 2020 International Conference on COMmunication Systems NETworkS (COMSNETS) (2020), pp. 306–313

  80. B. Aditya Prakash, A. Beutel, R. Rosenfeld, C. Faloutsos, Winner takes all: competing viruses or ideas on fair-play networks, in Proceedings of the 21st International Conference on World Wide Web, WWW ’12 (Association for Computing Machinery, New York, NY, USA, 2012), pp. 1037–1046

  81. M. Brede, How does active participation effect consensus: adaptive network model of opinion dynamics and influence maximizing rewiring. arXiv:1906.00868 (2019)

  82. P. Jia, A. MirTabatabaei, N. Friedkin, F. Bullo, Opinion dynamics and the evolution of social power in influence networks. SIAM Rev. 57(3), 367–397 (2015)

    MathSciNet  MATH  Google Scholar 

  83. R. Kang, C. Li, X. Li, Social power convergence on duplex influence networks with self-appraisals, in 2019 IEEE 58th Conference on Decision and Control (CDC) (2019), pp. 5611–5612

  84. N.E. Friedkin, P. Jia, F. Bullo, A theory of the evolution of social power: natural trajectories of interpersonal influence systems along issue sequences. Sociol. Sci. 3, 444–472 (2016)

    Google Scholar 

  85. P. Jia, N. Friedkin, F. Bullo, Opinion dynamics and social power evolution over reducible influence networks. SIAM J. Control Optim. 55(2), 1280–1301 (2017)

    MathSciNet  MATH  Google Scholar 

  86. M. Ye, B.D.O. Anderson, Modelling of individual behaviour in the Degroot–Friedkin self-appraisal dynamics on social networks, in 2019 18th European Control Conference (ECC) (2019), pp. 2011–2017

  87. M. Ye, J. Liu, B.D.O. Anderson, C. Yu, T. Başar, Evolution of social power in social networks with dynamic topology. IEEE Trans. Autom. Control 63(11), 3793–3808 (2018)

    MathSciNet  MATH  Google Scholar 

  88. Z. Askarzadeh, R. Fu, A. Halder, Y. Chen, T.T. Georgiou, Opinion dynamics over influence networks, in 2019 American Control Conference (ACC) (2019), pp. 1873–1878

  89. Z. Askarzadeh, R. Fu, A. Halder, Y. Chen, T.T. Georgiou, Stability theory of stochastic models in opinion dynamics. IEEE Trans. Autom. Control 65, 522–533 (2019)

    MATH  Google Scholar 

  90. Y. Tian, P. Jia, A. Mirtabatabaei, L. Wang, N.E. Friedkin, F. Bullo, Social power evolution in influence networks with stubborn individuals. arXiv:1901.08727 (2019)

  91. S. Galam, Stubbornness as an unfortunate key to win a public debate: an illustration from sociophysics. Mind Soc. 15(1), 117–130 (2016)

    Google Scholar 

  92. X. Chen, P. Tsaparas, J. Lijffijt, T. De Bie. Opinion dynamics with backfire effect and biased assimilation. arXiv:1903.11535 (2019)

  93. E. Kurmyshev, H.A. Juárez, R.A. González-Silva, Dynamics of bounded confidence opinion in heterogeneous social networks: concord against partial antagonism. Physica A Stat. Mech. Appl. 390(16), 2945–2955 (2011)

    ADS  Google Scholar 

  94. S. Huet, G. Deffuant, W. Jager, A rejection mechanism in 2d bounded confidence provides more conformity. Adv. Complex Syst. 11(04), 529–549 (2008)

    MathSciNet  MATH  Google Scholar 

  95. W. Jager, F. Amblard, Uniformity, bipolarization and pluriformity captured as generic stylized behavior with an agent-based simulation model of attitude change. Comput. Math. Org. Theory 10(4), 295–303 (2005)

    Google Scholar 

  96. C. Altafini, Dynamics of opinion forming in structurally balanced social networks, in Proceedings of the IEEE Conference on Decision and Control (2012)

  97. C. Altafini, Consensus problems on networks with antagonistic interactions. IEEE Trans. Autom. Control 58, 935–946 (2013)

    MathSciNet  MATH  Google Scholar 

  98. C. Altafini, F. Ceragioli, Signed bounded confidence models for opinion dynamics. Automatica 93, 114–125 (2018)

    MathSciNet  MATH  Google Scholar 

  99. S. Schweighofer, D. Garcia, F. Schweitzer, An agent-based model of multi-dimensional opinion dynamics and opinion alignment. arXiv:2003.05929 (2020)

  100. A.V. Proskurnikov, A.S. Matveev, M. Cao, Opinion dynamics in social networks with hostile camps: consensus vs. polarization. IEEE Trans. Autom. Control 61(6), 1524–1536 (2016)

    MathSciNet  MATH  Google Scholar 

  101. D. Bhat, S. Redner, Opinion formation under antagonistic influences. arXiv:1907.13103 (2019)

  102. G. He, J. Liu, H. Huimin, J.-A. Fang, Discrete-time signed bounded confidence model for opinion dynamics. Neurocomputing (2019). https://doi.org/10.1016/j.neucom.2019.12.061

    Article  Google Scholar 

  103. H. Zhang, J. Chen, Bipartite consensus of linear multi-agent systems over signed digraphs: an output feedback control approach, in IFAC Proceedings Volumes (IFAC-PapersOnline), vol. 19 (IFAC Secretariat, 2014), pp. 4681–4686

  104. D. Meng, Z. Meng, Y. Hong, Disagreement of hierarchical opinion dynamics with changing antagonisms. SIAM J. Control Optim. 57(1), 718–742 (2019)

    MathSciNet  MATH  Google Scholar 

  105. H.D. Aghbolagh, M. Zamani, S. Paolini, Z. Chen, Balance seeking opinion dynamics model based on social judgment theory. Physica D Nonlinear Phenom. 403, 132336 (2020)

    MathSciNet  Google Scholar 

  106. D. Cartwright, F. Harary, Structural balance: a generalization of heider’s theory. Psychol. Rev. 63(5), 277–293 (1956)

    Google Scholar 

  107. M. Mäs, A. Flache, D. Helbing, Individualization as driving force of clustering phenomena in humans. PLoS Comput. Biol. 6, 1000959 (2010)

    ADS  Google Scholar 

  108. The Division of Labour in Society (The Free Press, New York, 1893)

  109. S. Grauwin, P. Jensen, Opinion group formation and dynamics: structures that last from nonlasting entities. Phys. Rev. E. Stat. Nonlinear Soft Matter Phys. 85(6), 006113 (2012)

    Google Scholar 

  110. M. Pineda, R. Toral, E. Hernández-García, Diffusing opinions in bounded confidence processes. Eur. Phys. J. D 62(1), 109–117 (2011)

    ADS  Google Scholar 

  111. A. Carro, R. Toral, M.S. Miguel, The role of noise and initial conditions in the asymptotic solution of a bounded confidence, continuous-opinion model. J. Stat. Phys. 151(12), 131–149 (2013)

    ADS  MathSciNet  MATH  Google Scholar 

  112. W. Quattrociocchi, G. Caldarelli, A. Scala, Opinion dynamics on interacting networks: media competition and social influence. Sci. Rep. 4, 4938 (2014)

    ADS  Google Scholar 

  113. F. Baccelli, A. Chatterjee, S. Vishwanath, Pairwise stochastic bounded confidence opinion dynamics: heavy tails and stability. IEEE Trans. Autom. Control 62(11), 5678–5693 (2017)

    MathSciNet  MATH  Google Scholar 

  114. J. Zhang, Y. Zhao, The robust consensus of a noisy Deffuant–Weisbuch model. Math. Probl. Eng. 2018, 1065451 (2018)

    MathSciNet  MATH  Google Scholar 

  115. M. Pineda, R. Toral, E. Hernandez-Garcia, Noisy continuous-opinion dynamics. J. Stat. Mech. Theory Exp. 2009(08), P08001 (2009)

    MATH  Google Scholar 

  116. S. Wei, G. Chen, Y. Hong, Noise leads to quasi-consensus of Hegselmann–Krause opinion dynamics. Automatica 85, 448–454 (2017)

    MathSciNet  MATH  Google Scholar 

  117. G. Chen, W. Su, S. Ding, Y. Hong, Heterogeneous Hegselmann–Krause dynamics with environment and communication noise. IEEE Trans. Autom. Control, pp. 1–1 (2019). https://ieeexplore.ieee.org/document/8918332

  118. M. Pineda, R. Toral, E. Hernández-Garaćia, The noisy Hegselmann–Krause model for opinion dynamics. Eur. Phys. J. B 86(12), 490 (2013)

    ADS  MathSciNet  Google Scholar 

  119. B. Chazelle, Q. Jiu, Q. Li, C. Wang, Well-posedness of the limiting equation of a noisy consensus model in opinion dynamics. J. Differ. Equ. 263(1), 365–397 (2017)

    ADS  MathSciNet  MATH  Google Scholar 

  120. H. Liang, Y. Dong, C.-C. Li, Dynamics of uncertain opinion formation: an agent-based simulation. JASSS 19(4), 1–14 (2016)

    Google Scholar 

  121. H. Hamann, Opinion dynamics with mobile agents: contrarian effects by spatial correlations. Front. Robot. AI 5, 63 (2018)

    ADS  Google Scholar 

  122. L. Sabatelli, P. Richmond, Non-monotonic spontaneous magnetization in a Sznajd-like consensus model. Physica A 334(1), 274–280 (2004)

    ADS  Google Scholar 

  123. B.L. Granovsky, N. Madras, The noisy voter model. Stoch. Process. Appl. 55(1), 23–43 (1995)

    MathSciNet  MATH  Google Scholar 

  124. A. Carro, R. Toral, M.S. Miguel, The noisy voter model on complex networks. Sci. Rep. 6(1), 1–14 (2016)

    Google Scholar 

  125. A.F. Peralta, A. Carro, M. SanMiguel, R. Toral, Analytical and numerical study of the non-linear noisy voter model on complex networks. Chaos Interdiscip. J. Nonlinear Sci. 28(7), 075516 (2018)

    MathSciNet  Google Scholar 

  126. N.E. Friedkin, A.V. Proskurnikov, R. Tempo, S.E. Parsegov, Network science on belief system dynamics under logic constraints. Science 354(6310), 321–326 (2016)

    ADS  MathSciNet  MATH  Google Scholar 

  127. Y. Tian, L. Wang, Opinion dynamics in social networks with stubborn agents: an issue-based perspective. Automatica 96, 213–223 (2018)

    MathSciNet  MATH  Google Scholar 

  128. F. Xiong, Y. Liu, L. Wang, X. Wang, Analysis and application of opinion model with multiple topic interactions. Chaos Interdiscip. J. Nonlinear Sci. 27(8), 083113 (2017)

    MathSciNet  Google Scholar 

  129. H. Ahn, Q. Van Tran, M.H. Trinh, M. Ye, J. Liu, K.L. Moore, Opinion dynamics with cross-coupling topics: modeling and analysis. IEEE Trans. Comput. Soc. Syst. 7, 632–647 (2020)

    Google Scholar 

  130. W.S. Rossi, P. Frasca, Opinion dynamics with topological gossiping: Asynchronous updates under limited attention. IEEE Control Syst. Lett. 4(3), 566–571 (2020)

    Google Scholar 

  131. A. Fang, K. Yuan, J. Geng, X. Wei, Opinion dynamics with Bayesian learning. Complexity 2020, 1–5 (2020)

    Google Scholar 

  132. W. Wang, F. Chen, The opinion dynamics on the evolving complex network by achlioptas process. IEEE Access 7, 172928–172937 (2019)

    Google Scholar 

  133. A. Kowalska-Styczeń, K. Malarz, Opinion formation and spread: Does randomness of behaviour and information flow matter? arXiv:002.05451 (2020)

  134. M. Ye, Y. Qin, A. Govaert, B.D.O. Anderson, M. Cao, An influence network model to study discrepancies in expressed and private opinions. Automatica 107(7), 371–381 (2019)

    MathSciNet  MATH  Google Scholar 

  135. M.T. Gastner, B. Oborny, M. Gulyás, Consensus time in a voter model with concealed and publicly expressed opinions. J. Stat. Mech. Theory Exp. 2018(6), 063401 (2018)

    MathSciNet  Google Scholar 

  136. A. Jdrzejewski, G. Marcjasz, P.R. Nail, K. Sznajd-Weron, Think then act or act then think? PLoS One 13(11), 1–19 (2018)

    Google Scholar 

  137. N. Masuda, N. Gibert, S. Redner, Heterogeneous voter models. Phys. Rev. E 82, 010103 (2010)

    ADS  Google Scholar 

  138. S.-W. Wang, C.-Y. Huang, C.-T. Sun, Modeling self-perception agents in an opinion dynamics propagation society. Simulation 90(3), 238–248 (2014)

    Google Scholar 

  139. C.-Y. Huang, T.-H. Wen, A novel private attitude and public opinion dynamics model for simulating pluralistic ignorance and minority influence. J. Artif. Soc. Soc. Simul. 17(3), 8 (2014)

    Google Scholar 

  140. F.J. León-Medina, J. Tena-Sánchez, F.J. Miguel, Fakers becoming believers: how opinion dynamics are shaped by preference falsification, impression management and coherence heuristics. Qual Quant 4, 385–412 (2020)

    Google Scholar 

  141. Y. Shang, Consensus and clustering of expressed and private opinions in dynamical networks against attacks. IEEE Syst. J. 14(2), 2078–2084 (2020)

    ADS  Google Scholar 

  142. M. Afshar, M. Asadpour, Opinion formation by informed agents. JASSS 13(4), 5 (2010)

    Google Scholar 

  143. D. Li, D. Han, J. Ma, M. Sun, L. Tian, T. Khouw, H. EugeneStanley, Opinion dynamics in activity-driven networks. EPL 120, 28002 (2018)

    ADS  Google Scholar 

  144. Q. Liu, X. Wang, Opinion dynamics with similarity-based random neighbors. Sci. Rep. 3(1), 2968 (2013)

    ADS  Google Scholar 

  145. J. Zhang, Y. Hong, Opinion evolution analysis for short-range and long-range Deffuant–Weisbuch models. Physica A 392(21), 5289–5297 (2013)

    ADS  MathSciNet  MATH  Google Scholar 

  146. J. Zhang, Opinion limits study for the multi-selection bounded confidence model. PLoS One 14(1), e0210745 (2019)

    Google Scholar 

  147. H. Schawe, L. Hernández, When open mindedness hinders consensus. arXiv:2001.06877 (2020)

  148. Y.-P. Choi, A. Paolucci, C. Pignotti, Consensus of the Hegselmann–Krause opinion formation model with time delay. arXiv:1909.02795 (2019)

  149. G. Kou, Y. Zhao, Y. Peng, Y. Shi, Multi-level opinion dynamics under bounded confidence. PLoS ONE 7(9), e43507 (2012)

    ADS  Google Scholar 

  150. J.E. Rubio, R. Roman, J. Lopez, Integration of a threat traceability solution in the industrial internet of things. IEEE Trans. Ind. Inform. pp. 1–1 (2020). https://ieeexplore.ieee.org/document/9016083

  151. M. Kuhn, C. Kirse, H. Briesen, Population balance modeling and opinion dynamics—a mutually beneficial Liaison? Processes 6(9), 164 (2018)

    Google Scholar 

  152. S.Y. Pilyugin, M.C. Campi, Opinion formation in voting processes under bounded confidence. Netw. Heterog. Media 14(3), 617–632 (2019)

    MathSciNet  MATH  Google Scholar 

  153. D. Helbing, Boltzmann-like and Boltzmann–Fokker–Planck equations as a foundation of behavioral models. Physica A 196(4), 546–573 (1993)

    ADS  MathSciNet  MATH  Google Scholar 

  154. G. Toscani et al., Kinetic models of opinion formation. Commun. Math. Sci. 4(3), 481–496 (2006)

    MathSciNet  MATH  Google Scholar 

  155. L. Boudin, R. Monaco, F. Salvarani, A kinetic approach to the study of opinion formation. ESAIM Math. Model. Numer. Anal. 43(3), 507–522 (2009)

    MathSciNet  MATH  Google Scholar 

  156. S. Biswas, A. Chatterjee, P. Sen, Disorder induced phase transition in kinetic models of opinion dynamics. Physica A 391(11), 3257–3265 (2012)

    ADS  Google Scholar 

  157. L. Pareschi, P. Vellucci, M. Zanella, Kinetic models of collective decision-making in the presence of equality bias. Physica A 467, 201–217 (2017)

    ADS  MathSciNet  MATH  Google Scholar 

  158. M. Alexanian, D. McNamara, Anti-diffusion in continuous opinion dynamics. Physica A 503, 1256–1262 (2018)

    ADS  MathSciNet  Google Scholar 

  159. A.L. Oestereich, M.A. Pires, S.M. DuarteQueirós, N. Crokidakis, Hysteresis and disorder-induced order in continuous kinetic-like opinion dynamics in complex networks. arXiv:2002.09366 (2020)

  160. M. Lachowicz, H. Leszczyński, Modeling asymmetric interactions in economy. Mathematics 8(523), 1–24 (2020)

    Google Scholar 

  161. M. Fraia, A. Tosin, The Boltzmann legacy revisited: kinetic models of social interactions. arXiv:2003.14225 (2020)

  162. M. Lachowicz, H. Leszczyński, E. Puźniakowska-Gałuch, Diffusive and anti-diffusive behavior for kinetic models of opinion dynamics. Symmetry 11(8), 1024 (2019)

    Google Scholar 

  163. F. Welington, S. Lima, J.A. Plascak, Kinetic models of discrete opinion dynamics on directed Barabási–Albert networks. Entropy 21(10), 942 (2019)

    ADS  Google Scholar 

  164. L. Pareschi, G. Toscani, Interacting Multiagent Systems: Kinetic Equations and Monte Carlo Methods (Oxford University Press, Oxford, 2013)

    MATH  Google Scholar 

  165. B. Düring, P. Markowich, J.F. Pietschmann, M.T. Wolfram, Boltzmann and Fokker–Planck equations modeling opinion formation in the presence of strong leaders. Proc. R. Soc. Math. Phys. Eng. Sci. 465(2112), 3687–3708 (2009)

    ADS  MathSciNet  MATH  Google Scholar 

  166. P. Wang, J. Song, J. Huo, R. Hao, X.-M. Wang, Towards understanding what contributes to forming an opinion. Int. J. Mod. Phys. C 28(11), 28 (2017)

    Google Scholar 

  167. S. Biswas, A.K. Chandra, A. Chatterjee, B.K. Chakrabarti, Phase transitions and non-equilibrium relaxation in kinetic models of opinion formation. J. Phys. Conf. Ser. 297(1), 012004 (2011)

    Google Scholar 

  168. K.R. Chowdhury, A. Ghosh, S. Biswas, B.K. Chakrabarti, Kinetic exchange opinion model: solution in the single parameter map limit, in Econophysics of Agent-Based Models, ed. by F. Abergel, H. Aoyama, B.K. Chakrabarti, A. Chakraborti, A. Ghosh (Springer, Cham, 2014), pp. 131–143

    Google Scholar 

  169. L. Pareschi, M. Herty, G. Visconti, Mean field models for large data-clustering problems. arXiv preprint arXiv:1907.03585 (2019)

  170. B.-C. Wang, Y. Liang, Robust mean field social control problems with applications in analysis of opinion dynamics. arXiv:2002.12040 (2020)

  171. A. Chmiel, T. Gradowski, A. Krawiecki, q-neighbor ising model on random networks. Int. J. Mod. Phys. C 29(06), 1850041 (2018)

    ADS  MathSciNet  Google Scholar 

  172. L. Böttcher, J. Nagler, H.J. Herrmann, Critical behaviors in contagion dynamics. Phys. Rev. Lett. 118(8), 088301 (2017)

    ADS  Google Scholar 

  173. S. Biswas, P. Sen, A new model of binary opinion dynamics: coarsening and effect of disorder. arXiv preprint arXiv:0904.1498 (2009)

  174. S. Galam, Rational group decision making: a random field ising model at t = 0. Physica A 238(1–4), 66–80 (1997)

    ADS  Google Scholar 

  175. R. Abebe, J. Kleinberg, D. Parkes, C.E. Tsourakakis, Opinion dynamics with varying susceptibility to persuasion. arXiv:1801.07863 (2018)

  176. T.-H. Hubert Chan, Z. Liang, M. Sozio, Revisiting opinion dynamics with varying susceptibility to persuasion via non-convex local search, in The World Wide Web Conference, WWW ’19 (ACM, New York, NY, USA, 2019), pp. 173–183

  177. S. Patterson, B. Bamieh, Interaction-driven opinion dynamics in online social networks, in Proceedings of the First Workshop on Social Media Analytics, SOMA ’10 (ACM, New York, NY, USA, 2010), pp. 98–105

  178. H. Noorazar, M. Sottile, K. Vixie, Loss of community identity in opinion dynamics models as a function of inter-group interaction strength. CoRR arXiv:1708.03317 (2017)

  179. H. Noorazar, K.R. Vixie, A. Talebanpour, Y. Hu, From classical to modern opinion dynamics. arXiv:1909.12089 (2019)

  180. A.V. Proskurnikov, R. Tempo, A tutorial on modeling and analysis of dynamic social networks. Part II. Annu. Rev. Control 45, 166–190 (2018)

    MathSciNet  Google Scholar 

Download references

Acknowledgements

We would like to acknowledge the insightful inputs of Rainer Hegselmann and Mohammad Hossein Namaki that immeasurably helped in the development of this manuscript.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Hossein Noorazar.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Noorazar, H. Recent advances in opinion propagation dynamics: a 2020 survey. Eur. Phys. J. Plus 135, 521 (2020). https://doi.org/10.1140/epjp/s13360-020-00541-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/s13360-020-00541-2

Navigation