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A bibliometric analysis and basic model introduction of opinion dynamics

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Abstract

Information exchange and dissemination happen among individuals in a group or social network, which is an inevitable process before the formation of the group and individual opinions. Opinion dynamics is a multidisciplinary research field that models information/opinion exchange processes to simulate the dynamic of opinions in networks with different scales and features. The research on the dynamic of opinions is complex because the involved interactions with individuals are complicated. Many pieces of research and reviews have been conducted on relative models focusing on diverse aspects. Unlike the existing studies, this paper develops a bibliometric analysis and brief introduction of opinion dynamics by science mapping from a relatively macroscopical perspective. Bibliometrics tools such as VOS Viewer and Cite Space are applied to figure out the collaborative relationship networks of countries/regions, organizations, and authors, the bibliographic coupling analysis of documents, and the detection and clusters of keywords. A basic and brief introduction of the Ising model, Voter model, Majority model, Sznajd model, and Bounded confidence model are also given. This paper is propaedeutic material for readers who want to grasp the fundamental knowledge of opinion dynamics on what it is, how it develops, what the hotspots are, which articles to read, and what the cooperative relationship looks like.

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The data used to support the findings of this study is available from the corresponding author upon request.

References

  1. Castellano C, Fortunato S, Loreto V (2009) Statistical physics of social dynamics. Rev Mod Phys 81(2):591–646

  2. Lorenz J (2007) Continuous opinion dynamics under bounded confidence: a survey. Int J Mod Phys C 18(12):1819–1838

  3. Xia HX, Wang HL, Xuan ZG (2011) Opinion dynamics: a multidisciplinary review and perspective on future research. Int J Knowl Syst Sci 2(4):72–91

  4. Stauffer D (2013) A biased review of sociophysics. J Stat Phys 151(1–2):9–20

  5. Proskurnikov AV, Tempo R (2017) A tutorial on modeling and analysis of dynamic social networks. Part I. Annu Rev Control 43:65–79

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

  7. Jalili M, Perc M (2017) Information cascades in complex networks. J Complex Netw 5(5):665–693

  8. Sznajd-Weron K, Sznajd J, Weron T (2021) A review on the Sznajd model-20 years after. Phys A 565:125537

  9. Sobkowicz P (2020) Whither now, opinion modelers? Front Phys-Lausanne 8:587009

  10. Patil A, Shah GT (2020) Multi-robot trajectory tracking and rendezvous algorithm. IETE J Res. https://doi.org/10.1080/03772063.2020.1800521

  11. Aylaj B, Bellomo N, Chouhad N, Knopoff D (2021) On the interaction between soft and hard sciences: the role of mathematical sciences looking ahead to research perspectives. Vietnam J Math 49(1):3–20

  12. Maghenem M, Postoyan R, Loria A, Panteley E (2020) Lyapunov-based synchronization of networked systems: from continuous-time to hybrid dynamics. Annu Rev Control 50:335–342

  13. Proskurnikov AV, Calafiore GC, Cao M (2020) Recurrent averaging inequalities in multi-agent control and social dynamics modeling. Annu Rev Control 49:95–112

  14. Tena-Sanchez J, Leon-Medina FJ (2019) Models of the dynamics of opinion. A literature review. Rev Int Sociol 77(2):e123

  15. Anderson BDO, Ye MB (2019) Recent advances in the modelling and analysis of opinion dynamics on influence networks. Int J Autom Comput 16(2):129–149

  16. Zha QB, Kou G, Zhang HJ, Liang HM, Chen X, Li CC, Dong YC (2021) Opinion dynamics in finance and business: a literature review and research opportunities. Financ Innov 6(1):44

  17. Ma SY, Zhang HZ (2021) Opinion expression dynamics in social media chat groups: An integrated Quasi-experimental and agent-based model approach. Complexity 2021:2304754

  18. Noorazar H (2020) Recent advances in opinion propagation dynamics: a 2020 survey. Eur Phys J Plus 135(6):521

  19. Camilleri AR (2020) The importance of online reviews depends on when they are presented. Decis Support Syst 133:113307

  20. Yu DJ, Xu ZS, Pedrycz W, Wang WR (2017) Information sciences 1968–2016: a retrospective analysis with text mining and bibliometric. Inf Sci 418:619–634

  21. Wang XX, Chang YR, Xu ZS, Wang ZD, Kadirkamanathan V (2021) 50 years of international journal of systems science: a review of the past and trends for the future. Int J Syst Sci 52(8):1515–1538

  22. Landstrom H, Harirchi G, Astrom F (2012) Entrepreneurship: exploring the knowledge base. Res Policy 41(7):1154–1181

  23. Cancino CA, Merigo JM, Coronado FC (2017) A bibliometric analysis of leading universities in innovation research. J Innov Knowl 2(3):106–124

  24. Yu DJ, Xu ZS, Fujita H (2019) Bibliometric analysis on the evolution of applied intelligence. Appl Intell 49(2):449–462

  25. Xu ZS, Lei TT, Qin Y (2022) An overview of probabilistic preference decision-making based on bibliometric analysis. Appl Intell. https://doi.org/10.1007/s10489-022-03189-w:19

  26. Cobo MJ, Martinez MA, Gutierrez-Salcedo M, Fujita H, Herrera-Viedma E (2015) 25 years at knowledge-based Systems: a bibliometric analysis. Knowl-Based Syst 80:3–13

  27. Li Y, Xu ZS, Wang XX, Filip FG (2019) Studies in Informatics and Control: a bibliometric analysis from 2008 to 2019. Int J Comput Commun 14(6):633–652

  28. Glanzel W, Czerwon HJ (1996) A new methodological approach to bibliographic coupling and its application to the national, regional and institutional level. Scientometrics 37(2):195–221

  29. Sousa AO, Malarz K, Galam S (2005) Reshuffling spins with short range interactions: when sociophysics produces physical results. Int J Mod Phys C 16(10):1507–1517

  30. Stauffer D (2005) Sociophysics simulations II: opinion dynamics. In: 8th Granada Seminar, pp 56–68

  31. Dall’Asta L, Baronchelli A, Barrat A, Loreto V (2006) Nonequilibrium dynamics of language games on complex networks. Phys Rev E 74(3):036105

  32. Yang HX, Wu ZX, Zhou CS, Zhou T, Wang BH (2009) Effects of social diversity on the emergence of global consensus in opinion dynamics. Phys Rev E 80(4):046108

  33. Hu K, Tang Y (2009) Consensus formation in weighted scale-free networks. Int J Mod Phys C 20(5):677–686

  34. Hegselmann R, Krause U (2002) Opinion dynamics and bounded confidence: models, analysis and simulation. JASSS-J Artif Soc S 5(3):2

  35. Hegselmann R, Krause U (2006) Truth and cognitive division of labour first steps towards a computer aided social epistemology. JASSS-J Artif Soc S 9(3):10

  36. Pilyugin SY, Campi MC (2019) Opinion formation in voting processes under bounded confidence. Netw Heterog Media 14(3):617–632

  37. Bortot S, Pereira RAM, Stamatopoulou A (2020) Consensus dynamics, network interaction, and Shapley indices in the Choquet framework. Soft Comput 24(18):13757–13768

  38. Baum MA, Kernell S (2001) Economic class and popular support for Franklin Roosevelt in war and peace. Public Opin Quart 65(2):198–229

  39. Vliegenthart R, Schuck ART, Boomgaarden HG, De Vreese CH (2008) News coverage and support for european integration, 1990–2006. Int J Public Opin R 20(4):415–439

  40. Biondi Y, Giannoccolo P, Galam S (2012) Formation of share market prices under heterogeneous beliefs and common knowledge. Phys A 391(22):5532–5545

  41. Vaidya T, Murguia C, Piliouras G (2020) Learning agents in Black-Scholes financial markets. Roy Soc Open Sci 7(10):201188

  42. Patriarca M, Heinsalu E, Singh A, Chakraborti A (2017) Kinetic exchange models as D dimensional systems: A comparison of different approaches. In: International Workshop on Econophysics and Sociophysics - Recent Progress and Future Directions (Econophys), pp 147–158. https://doi.org/10.1007/978-3-319-47705-3_11

  43. Crokidakis N (2014) A three-state kinetic agent-based model to analyze tax evasion dynamics. Phys A 414:321–328

  44. De Vreese CH, Boomgaarden HG (2006) Media message flows and interpersonal communication - the conditional nature of effects on public opinion. Commun Res 33(1):19–37

  45. Ali RN, Rubin H, Sarkar S (2021) Countering the potential re-emergence of a deadly infectious disease-information warfare, identifying strategic threats, launching countermeasures. PLoS ONE 16(8):e0256014

  46. Kandiah V, Binder AR, Berglund EZ (2017) An empirical agent-based model to simulate the adoption of water reuse using the social amplification of risk framework. Risk Anal 37(10):2005–2022

  47. Kandiah VK, Berglund EZ, Binder AR (2019) An agent-based modeling approach to project adoption of water reuse and evaluate expansion plans within a sociotechnical water infrastructure system. Sustain Cities Soc 46:101412

  48. Deffuant G, Neau D, Amblard F, Weisbuch G (2000) Mixing beliefs among interacting agents. Appl Simul Soc Sci 87–98. https://doi.org/10.1142/S0219525900000078

  49. Krapivsky PL, Redner S (2003) Dynamics of majority rule in two-state interacting spin systems. Phys Rev Lett 90(23):238701

  50. Acemoglu D, Ozdaglar A (2011) Opinion dynamics and learning in social networks. Dyn Games Appl 1(1):3–49

  51. Galam S (2008) Sociophysics: a review of Galam models. Int J Mod Phys C 19(3):409–440

  52. Blondel VD, Hendrickx JM, Tsitsiklis JN (2009) On Krause’s multi-agent consensus model with state-dependent connectivity. IEEE T Automat Contr 54(11):2586–2597

  53. Motsch S, Tadmor E (2014) Heterophilious dynamics enhances consensus. SIAM Rev 56(4):577–621

  54. Galam S (2004) Contrarian deterministic effects on opinion dynamics: “the hung elections scenario”. Phys A 333:453–460

  55. Kiesling E, Gunther M, Stummer C, Wakolbinger LM (2012) Agent-based simulation of innovation diffusion: a review. Cent Eur J Oper Res 20(2):183–230

  56. van der Linden S, Leiserowitz A, Rosenthal S, Maibach E (2017) Inoculating the public against misinformation about climate change. Glob Chall 1(2):1600008

  57. Weidlich W (1971) The statistical description of polarization phenomena in society. Br J Math & Stat Psychol 24(2):251–266

  58. Xie ZP, Song X, Li QY (2016) A review of opinion dynamics. In: Joint Conference of the 16th Asia Simulation Conference / SCS International Autumn Simulation Multi-Conference (AsiaSim/SCS AutumnSim), pp 349–357. https://doi.org/10.1007/978-981-10-2672-0_36

  59. Shukla P (2018) Hysteresis in the zero-temperature random-field ising model on directed random graphs. Phys Rev E 98(3):032144

  60. Li LB, Fan Y, Zeng A, Di ZR (2019) Binary opinion dynamics on signed networks based on Ising model. Phys A 525:433–442

  61. Smug D, Sornette D, Ashwin P (2018) A generalized 2D-dynamical mean-field ising model with a rich set of bifurcations (inspired and applied to financial crises). Int J Bifurcat Chaos 28(4):1830010

  62. des Mesnards NG, Hunter DS, el Hjouji Z, Zaman T (2022) Detecting bots and assessing their impact in social networks. Oper Res 70(1):1–22

  63. Tiwari M, Yang XG, Sen S (2021) Modeling the nonlinear effects of opinion kinematics in elections: a simple ising model with random field based study. Phys A 582:126287

  64. Clifford P, Sudbury A (1973) A model for spatial conflict. Biometrika 60(3):581–588

  65. Holley RA, Liggett TM (1975) Ergodic theorems for weakly interacting infinite systems and voter model. Ann Probab 3(4):643–663

  66. Zschaler G (2012) Adaptive-network models of collective dynamics. Eur Phys J-Spec Top 211(1):1–101

  67. Klamser PP, Wiedermann M, Donges JF, Donner RV (2017) Zealotry effects on opinion dynamics in the adaptive voter model. Phys Rev E 96(5):052315

  68. Majmudar JR, Krone SM, Baumgaertner BO, Tyson RC (2020) Voter models and external influence. J Math Sociol 44(1):1–11

  69. Khalil N, Toral R (2019) The noisy voter model under the influence of contrarians. Phys A 515:81–92

  70. Kononovicius A (2021) Supportive interactions in the noisy voter model. Chaos Soliton Fract 143:110627

  71. Khalil N, Galla T (2021) Zealots in multistate noisy voter models. Phys Rev E 103(1):012311

  72. Ma WK, Liu XS, Guan JY (2021) Consensus time in a concealed voter model with heterogeneous activity of voters. Int J Mod Phys C 32(11):2150151

  73. Jedrzejewski A, Sznajd-Weron K (2022) Pair approximation for the q-voter models with quenched disorder on networks. Phys Rev E 105(6):064306

  74. Abramiuk A, Sznajd-Weron K (2020) Generalized independence in the q-Voter Model: how do parameters influence the phase transition? Entropy-Switz 22(1):120

  75. Abramiuk A, Pawlowski J, Sznajd-Weron K (2019) Is independence necessary for a discontinuous phase transition within the q-voter model? Entropy-Switz 21(5):521

  76. Jedrzejewski A, Sznajd-Weron K (2019) Statistical physics of opinion formation: is it a SPOOF? Cr Phys 20(4):244–261

  77. Chmiel A, Sienkiewicz J, Fronczak A, Fronczak P (2020) A veritable zoology of successive phase transitions in the ssymmetric q-voter model on multiplex networks. Entropy-Switz 22(9):1018

  78. Vieira AR, Anteneodo C (2018) Threshold q-voter model. Phys Rev E 97(5):052106

  79. Chiyomaru K, Takemoto K (2022) Adversarial attacks on voter model dynamics in complex networks. Phys Rev E 106(1):014301

  80. Nowak B, Ston B, Sznajd-Weron K (2021) Discontinuous phase transitions in the multi-state noisy q-voter model: quenched vs. annealed disorder. Sci Rep-Uk 11(1):6098

  81. Moreno GR, Manino E, Long TT, Brede M (2020) Zealotry and Influence Maximization in the Voter Model: When to Target Partial Zealots? In: 11th International Conference on Complex Networks (CompleNet), pp 107–118. https://doi.org/10.1007/978-3-030-40943-2_10

  82. Jedrzejewski A, Sznajd-Weron K (2018) Impact of memory on opinion dynamics. Phys A 505:306–315

  83. Galam S (2002) Minority opinion spreading in random geometry. Eur Phys J B 25(4):403–406

  84. Chen P, Redner S (2005) Majority rule dynamics in finite dimensions. Phys Rev E 71(3):036101

  85. Mobilia M, Redner S (2003) Majority versus minority dynamics: phase transition in an interacting two-state spin system. Phys Rev E 68(4):046106

  86. Campos PRA, de Oliveira VM, Moreira FGB (2003) Small-world effects in the majority-vote model. Phys Rev E 67(2):026104

  87. Mukhopadhyay A, Mazumdar RR, Roy R (2016) Binary opinion dynamics with biased agents and agents with different degrees of stubbornness. In: 28th International Teletraffic Congress (ITC), pp 261–269

  88. Mukhopadhyay A, Mazumdar RR, Roy R (2020) Voter and majority dynamics with biased and stubborn agents. J Stat Phys 181(4):1239–1265

  89. Shekatkar SM (2020) Do zealots increase or decrease the polarization of social networks? J Complex Netw 8(4):cnz036

  90. Martinez FG, Balankin A (2021) Majority rule dynamics between a double coalition and a third opinion: coalition profit models and majority coalition ties. Adapt Behav 29(4):333–347

  91. Sznajd-Weron K, Sznajd J (2000) Opinion evolution in closed community. Int J Mod Phys C 11(6):1157–1165

  92. Stauffer D, Sousa AO, De Oliveira SM (2000) Generalization to square lattice of Sznajd sociophysics model. Int J Mod Phys C 11(6):1239–1245

  93. Behera L, Schweitzer F (2003) On spatial consensus formation: is the Sznajd model different from a voter model? Int J Mod Phys C 14(10):1331–1354

  94. Calvelli M, Crokidakis N, Penna TJP (2019) Phase transitions and universality in the Sznajd model with anticonformity. Phys A 513:518–523

  95. Muslim R, Anugraha R, Sholihun S, Rosyid MF (2020) Phase transition of the Sznajd model with anticonformity for two different agent configurations. Int J Mod Phys C 31(4):2050052

  96. Schneider JJ, Hirtreiter C (2005) The impact of election results on the member numbers of the large parties in Bavaria and Germany. Int J Mod Phys C 16(8):1165–1215

  97. Vannucchi FS, Prado CPC (2009) Sznajd model and proportional elections: the role of the topology of the network. Int J Mod Phys C 20(6):979–990

  98. Luo Y, Li YK, Sun CD, Cheng C (2022) Adapted Deffuant-Weisbuch model with implicit and explicit opinions. Phys A 596:127095

  99. Zhang JB, Zhao YY (2018) The robust consensus of a noisy Deffuant-Weisbuch model. Math Probl Eng 2018:1065451

  100. Su W, Chen XZ, Yu YG, Chen G (2022) Noise-based control of opinion dynamics. IEEE T Automat Contr 67(6):3134–3140

  101. Piccoli B, Rossi F (2021) Generalized solutions to bounded-confidence models. Math Mod Meth Appl S 31(06):1237–1276

  102. Vasca F, Bernardo C, Iervolino R (2021) Practical consensus in bounded confidence opinion dynamics. Automatica 129:109683

  103. Hou J, Li WS, Jiang MY (2021) Opinion dynamics in modified expressed and private model with bounded confidence. Phys A 574:125968

  104. Zou F, Li YP, Huang JH (2020) Group interaction and evolution of customer reviews based on opinion dynamics towards product redesign. Electron Commer Res. https://doi.org/10.1007/s10660-020-09447-8

  105. Chen G, Su W, Mei WJ, Bullo F (2020) Convergence properties of the heterogeneous deffuant-weisbuch model. Automatica 114:108825

  106. Douven I (2019) Optimizing group learning: an evolutionary computing approach. Artif Intell 275:235–251

  107. Almeida R, Girejko E, Machado L, Malinowska AB, Martins N (2018) Application of predictive control to the Hegselmann-Krause model. Math Method Appl Sci 41(18):9191–9202

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This study was funded by the National Natural Science Foundation of China (No. 72071135).

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Li, Y., Xu, Z. A bibliometric analysis and basic model introduction of opinion dynamics. Appl Intell 53, 16540–16559 (2023). https://doi.org/10.1007/s10489-022-04368-5

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