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.
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References
J.R.P. French Jr., A formal theory of social power. Psychol. Rev. 63(3), 181–194 (1956)
M. DeGroot, Reaching a consensus. J. Am. Stat. Assoc. 69(345), 118–121 (1974)
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)
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)
A. Mukhopadhyay, R.R. Mazumdar, R. Roy, Opinion dynamics under voter and majority rule models with biased and stubborn agents. arXiv:2003.02885 (2020)
G. Deffuant, D. Neau, F. Amblard, G. Weisbuch, Mixing beliefs among interacting agents. Adv. Complex Syst. 03(01n04), 87–98 (2000)
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)
A.C.R. Martins, Continuous opinions and discrete actions in opinion dynamics problems. Int. J. Mod. Phys. C 19(4), 617–624 (2007)
A.C.R. Martins, Discrete opinion dynamics with M choices. Eur. Phys. J. B 93(1), 1 (2020)
Y. Yi, S. Patterson, Disagreement and polarization in two-party social networks. arXiv:1911.11338 (2019)
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)
O. Abrahamsson, D. Danev, E.G. Larsson, Opinion dynamics with random actions and a stubborn agent. arXiv:1912.04183 (2019)
F. Jacobs, S. Galam, Two-opinions-dynamics generated by inflexibles and non-contrarian and contrarian floaters. Adv. Complex Syst. 22(04), 1950008 (2019)
S. Galam, F. Jacobs, The role of inflexible minorities in the breaking of democratic opinion dynamics. Physica A 381, 366–376 (2007)
B. Chazelle, C. Wang, Inertial Hegselmann–Krause systems. IEEE Trans. Autom. Control 62(8), 3905–3913 (2017)
J. Lorenz, Heterogeneous bounds of confidence: meet, discuss and find consensus!. Complexity 15(4), 43–52 (2010)
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)
N. Friedkin, E. Johnsen, Social influence and opinions. J. Math. Sociol. 15, 193–206 (1990)
N. Friedkin, E. Johnsen, Social influence networks and opinion change models of opinion formation. Adv. Group Process. 16, 1–29 (1999)
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)
R. Hegselmann, U. Krause, Opinion dynamics and bounded confidence: models, analysis and simulation. J. Artif. Soc. Soc. Simul. 5(3), 1–30 (2002)
P. Sobkowicz, Extremism without extremists: Deffuant model with emotions. Front. Phys. 3, 17 (2015)
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)
C. Castellano, S. Fortunato, V. Loreto, Statistical physics of social dynamics. Rev. Mod. Phys. 81(2), 591 (2009)
G. Chen, W. Su, W. Mei, F. Bullo, Convergence properties of the heterogeneous Deffuant–Weisbuch model. arXiv:1901.02092 (2019)
J. Zhang, G. Chen, Convergence rate of the asymmetric Deffuant–Weisbuch dynamics. J. Syst. Sci. Complex. 28(4), 773–787 (2015)
Y. Shang, An agent based model for opinion dynamics with random confidence threshold. Commun. Nonlinear Sci. Numer. Simul. 19(10), 3766–3777 (2014)
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)
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
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)
S. Galam, The Trump phenomenon: an explanation from sociophysics. Int. J. Mod. Phys. B 31(10), 1742015 (2017)
S. Biswas, P. Sen, Critical noise can make the minority candidate win: the US presidential election cases. Phys. Rev. E 96(3), 032303 (2017)
N.E. Friedkin, A formal theory of social power. J. Math. Sociol. 12(2), 103–126 (1986)
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)
S. Galam, Majority rule, hierarchical structures, and democratic totalitarianism: a statistical approach. J. Math. Psychol. 30(4), 426–434 (1986)
S. Galam, Sociophysics: a review of galam models. Int. J. Mod. Phys. C 19(03), 409–440 (2008)
S. Galam, Sociophysics, A Physicist’s Modeling of Psycho-political Phenomena (Springer, New York, 2012)
B. Gärtner, A.N. Zehmakan, Threshold behavior of democratic opinion dynamics. J. Stat. Phys. 178, 1442–1466 (2020)
K. Sznajd-Weron, J. Sznajd, Opinion evolution in closed community. Int. J. Mod. Phys. C 11(06), 1157–1165 (2000)
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)
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)
M. Calvelli, N. Crokidakis, T.J.P. Penna, Phase transitions and universality in the Sznajd model with anticonformity. Physica A 513, 518–523 (2019)
K. Sznajd-Weron, Sznajd model and its applications. arXiv:physics/0503239v1 (2005)
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
V. Sood, S. Redner, Voter model on heterogeneous graphs. Phys. Rev. Lett. 94(17), 178701 (2005)
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)
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)
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)
S. Redner, Reality-inspired voter models: a mini-review. C. R. Phys. 20(4), 275–292 (2019)
H. Wai, A. Scaglione, A. Leshem, Active sensing of social networks. IEEE Trans. Signal Inf. Process. Netw. 2(3), 406–419 (2016)
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)
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
T. Cheon, S. Galam, Dynamical galam model. Phys. Lett. A 382(23), 1509–1515 (2018)
S. Galam, T. Cheon, Tipping point dynamics: a universal formula. arXiv:1901.09622 (2019)
S. Qian, Y. Liu, S. Galam, Activeness as a key to counter democratic balance. Physica A 432, 187–196 (2015)
T. Cheon, J. Morimoto, Balancer effects in opinion dynamics. Phys. Lett. A 380(3), 429–434 (2016)
S. Galam, T. Cheon, Asymmetric contrarians in opinion dynamics. Entropy 22(1), 25 (2020)
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)
N. Khalil, M. San Miguel, R. Toral, Zealots in the mean-field noisy voter model. Phys. Rev. E 97, 012310 (2018)
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)
P. Dandekar, A. Goel, D.T. Lee, Biased assimilation, homophily, and the dynamics of polarization. Proc. Natl. Acad. Sci. 110(15), 5791–5796 (2013)
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)
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)
X. Chen, X. Zhang, Y. Xie, W. Li, Opinion dynamics of social-similarity-based Hegselmann–Krause model. Complexity 2017, 1820257 (2017)
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)
Y. Dong, Z. Ding, L. Martínez, F. Herrera, Managing consensus based on leadership in opinion dynamics. Inf. Sci. 397–398, 187–205 (2017)
M. Pineda, G.M. Buendía, Mass media and heterogeneous bounds of confidence in continuous opinion dynamics. Physica A 420, 73–84 (2015)
D. Bauso, M. Cannon, Consensus in opinion dynamics as a repeated game. Automatica 90, 204–211 (2018)
R. Hegselmann, S. König, S. Kurz, C. Niemann, J. Rambau, Optimal opinion control: the campaign problem. arXiv preprint arXiv:1410.8419 (2014)
J. Gaitonde, J. Kleinberg, E. Tardos, Adversarial perturbations of opinion dynamics in networks. arXiv:2003.07010 (2020)
T. Carletti, D. Fanelli, S. Grolli, A. Guarino, How to make an efficient propaganda. Europhys. Lett. 74(2), 222–228 (2006)
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)
A. Gupta, S. Moharir, N. Sahasrabudhe, Influencing opinion dynamics in networks with limited interaction. arXiv:2002.00664 (2020)
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
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)
R. Hegselmann, S. König, S. Kurz, C. Niemann, J. Rambau, Optimal opinion control: the campaign problem. Jasss 18(3), 1–40 (2015)
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)
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)
M. Goyal, D. Manjunath, Opinion control competition in a social network. In 2020 International Conference on COMmunication Systems NETworkS (COMSNETS) (2020), pp. 306–313
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
M. Brede, How does active participation effect consensus: adaptive network model of opinion dynamics and influence maximizing rewiring. arXiv:1906.00868 (2019)
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)
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
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)
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)
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
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)
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
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)
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)
S. Galam, Stubbornness as an unfortunate key to win a public debate: an illustration from sociophysics. Mind Soc. 15(1), 117–130 (2016)
X. Chen, P. Tsaparas, J. Lijffijt, T. De Bie. Opinion dynamics with backfire effect and biased assimilation. arXiv:1903.11535 (2019)
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)
S. Huet, G. Deffuant, W. Jager, A rejection mechanism in 2d bounded confidence provides more conformity. Adv. Complex Syst. 11(04), 529–549 (2008)
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)
C. Altafini, Dynamics of opinion forming in structurally balanced social networks, in Proceedings of the IEEE Conference on Decision and Control (2012)
C. Altafini, Consensus problems on networks with antagonistic interactions. IEEE Trans. Autom. Control 58, 935–946 (2013)
C. Altafini, F. Ceragioli, Signed bounded confidence models for opinion dynamics. Automatica 93, 114–125 (2018)
S. Schweighofer, D. Garcia, F. Schweitzer, An agent-based model of multi-dimensional opinion dynamics and opinion alignment. arXiv:2003.05929 (2020)
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)
D. Bhat, S. Redner, Opinion formation under antagonistic influences. arXiv:1907.13103 (2019)
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
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
D. Meng, Z. Meng, Y. Hong, Disagreement of hierarchical opinion dynamics with changing antagonisms. SIAM J. Control Optim. 57(1), 718–742 (2019)
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)
D. Cartwright, F. Harary, Structural balance: a generalization of heider’s theory. Psychol. Rev. 63(5), 277–293 (1956)
M. Mäs, A. Flache, D. Helbing, Individualization as driving force of clustering phenomena in humans. PLoS Comput. Biol. 6, 1000959 (2010)
The Division of Labour in Society (The Free Press, New York, 1893)
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)
M. Pineda, R. Toral, E. Hernández-García, Diffusing opinions in bounded confidence processes. Eur. Phys. J. D 62(1), 109–117 (2011)
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)
W. Quattrociocchi, G. Caldarelli, A. Scala, Opinion dynamics on interacting networks: media competition and social influence. Sci. Rep. 4, 4938 (2014)
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)
J. Zhang, Y. Zhao, The robust consensus of a noisy Deffuant–Weisbuch model. Math. Probl. Eng. 2018, 1065451 (2018)
M. Pineda, R. Toral, E. Hernandez-Garcia, Noisy continuous-opinion dynamics. J. Stat. Mech. Theory Exp. 2009(08), P08001 (2009)
S. Wei, G. Chen, Y. Hong, Noise leads to quasi-consensus of Hegselmann–Krause opinion dynamics. Automatica 85, 448–454 (2017)
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
M. Pineda, R. Toral, E. Hernández-Garaćia, The noisy Hegselmann–Krause model for opinion dynamics. Eur. Phys. J. B 86(12), 490 (2013)
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)
H. Liang, Y. Dong, C.-C. Li, Dynamics of uncertain opinion formation: an agent-based simulation. JASSS 19(4), 1–14 (2016)
H. Hamann, Opinion dynamics with mobile agents: contrarian effects by spatial correlations. Front. Robot. AI 5, 63 (2018)
L. Sabatelli, P. Richmond, Non-monotonic spontaneous magnetization in a Sznajd-like consensus model. Physica A 334(1), 274–280 (2004)
B.L. Granovsky, N. Madras, The noisy voter model. Stoch. Process. Appl. 55(1), 23–43 (1995)
A. Carro, R. Toral, M.S. Miguel, The noisy voter model on complex networks. Sci. Rep. 6(1), 1–14 (2016)
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)
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)
Y. Tian, L. Wang, Opinion dynamics in social networks with stubborn agents: an issue-based perspective. Automatica 96, 213–223 (2018)
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)
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)
W.S. Rossi, P. Frasca, Opinion dynamics with topological gossiping: Asynchronous updates under limited attention. IEEE Control Syst. Lett. 4(3), 566–571 (2020)
A. Fang, K. Yuan, J. Geng, X. Wei, Opinion dynamics with Bayesian learning. Complexity 2020, 1–5 (2020)
W. Wang, F. Chen, The opinion dynamics on the evolving complex network by achlioptas process. IEEE Access 7, 172928–172937 (2019)
A. Kowalska-Styczeń, K. Malarz, Opinion formation and spread: Does randomness of behaviour and information flow matter? arXiv:002.05451 (2020)
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)
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)
A. Jdrzejewski, G. Marcjasz, P.R. Nail, K. Sznajd-Weron, Think then act or act then think? PLoS One 13(11), 1–19 (2018)
N. Masuda, N. Gibert, S. Redner, Heterogeneous voter models. Phys. Rev. E 82, 010103 (2010)
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)
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)
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)
Y. Shang, Consensus and clustering of expressed and private opinions in dynamical networks against attacks. IEEE Syst. J. 14(2), 2078–2084 (2020)
M. Afshar, M. Asadpour, Opinion formation by informed agents. JASSS 13(4), 5 (2010)
D. Li, D. Han, J. Ma, M. Sun, L. Tian, T. Khouw, H. EugeneStanley, Opinion dynamics in activity-driven networks. EPL 120, 28002 (2018)
Q. Liu, X. Wang, Opinion dynamics with similarity-based random neighbors. Sci. Rep. 3(1), 2968 (2013)
J. Zhang, Y. Hong, Opinion evolution analysis for short-range and long-range Deffuant–Weisbuch models. Physica A 392(21), 5289–5297 (2013)
J. Zhang, Opinion limits study for the multi-selection bounded confidence model. PLoS One 14(1), e0210745 (2019)
H. Schawe, L. Hernández, When open mindedness hinders consensus. arXiv:2001.06877 (2020)
Y.-P. Choi, A. Paolucci, C. Pignotti, Consensus of the Hegselmann–Krause opinion formation model with time delay. arXiv:1909.02795 (2019)
G. Kou, Y. Zhao, Y. Peng, Y. Shi, Multi-level opinion dynamics under bounded confidence. PLoS ONE 7(9), e43507 (2012)
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
M. Kuhn, C. Kirse, H. Briesen, Population balance modeling and opinion dynamics—a mutually beneficial Liaison? Processes 6(9), 164 (2018)
S.Y. Pilyugin, M.C. Campi, Opinion formation in voting processes under bounded confidence. Netw. Heterog. Media 14(3), 617–632 (2019)
D. Helbing, Boltzmann-like and Boltzmann–Fokker–Planck equations as a foundation of behavioral models. Physica A 196(4), 546–573 (1993)
G. Toscani et al., Kinetic models of opinion formation. Commun. Math. Sci. 4(3), 481–496 (2006)
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)
S. Biswas, A. Chatterjee, P. Sen, Disorder induced phase transition in kinetic models of opinion dynamics. Physica A 391(11), 3257–3265 (2012)
L. Pareschi, P. Vellucci, M. Zanella, Kinetic models of collective decision-making in the presence of equality bias. Physica A 467, 201–217 (2017)
M. Alexanian, D. McNamara, Anti-diffusion in continuous opinion dynamics. Physica A 503, 1256–1262 (2018)
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)
M. Lachowicz, H. Leszczyński, Modeling asymmetric interactions in economy. Mathematics 8(523), 1–24 (2020)
M. Fraia, A. Tosin, The Boltzmann legacy revisited: kinetic models of social interactions. arXiv:2003.14225 (2020)
M. Lachowicz, H. Leszczyński, E. Puźniakowska-Gałuch, Diffusive and anti-diffusive behavior for kinetic models of opinion dynamics. Symmetry 11(8), 1024 (2019)
F. Welington, S. Lima, J.A. Plascak, Kinetic models of discrete opinion dynamics on directed Barabási–Albert networks. Entropy 21(10), 942 (2019)
L. Pareschi, G. Toscani, Interacting Multiagent Systems: Kinetic Equations and Monte Carlo Methods (Oxford University Press, Oxford, 2013)
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)
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)
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)
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
L. Pareschi, M. Herty, G. Visconti, Mean field models for large data-clustering problems. arXiv preprint arXiv:1907.03585 (2019)
B.-C. Wang, Y. Liang, Robust mean field social control problems with applications in analysis of opinion dynamics. arXiv:2002.12040 (2020)
A. Chmiel, T. Gradowski, A. Krawiecki, q-neighbor ising model on random networks. Int. J. Mod. Phys. C 29(06), 1850041 (2018)
L. Böttcher, J. Nagler, H.J. Herrmann, Critical behaviors in contagion dynamics. Phys. Rev. Lett. 118(8), 088301 (2017)
S. Biswas, P. Sen, A new model of binary opinion dynamics: coarsening and effect of disorder. arXiv preprint arXiv:0904.1498 (2009)
S. Galam, Rational group decision making: a random field ising model at t = 0. Physica A 238(1–4), 66–80 (1997)
R. Abebe, J. Kleinberg, D. Parkes, C.E. Tsourakakis, Opinion dynamics with varying susceptibility to persuasion. arXiv:1801.07863 (2018)
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
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
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)
H. Noorazar, K.R. Vixie, A. Talebanpour, Y. Hu, From classical to modern opinion dynamics. arXiv:1909.12089 (2019)
A.V. Proskurnikov, R. Tempo, A tutorial on modeling and analysis of dynamic social networks. Part II. Annu. Rev. Control 45, 166–190 (2018)
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We would like to acknowledge the insightful inputs of Rainer Hegselmann and Mohammad Hossein Namaki that immeasurably helped in the development of this manuscript.
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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
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DOI: https://doi.org/10.1140/epjp/s13360-020-00541-2