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A Dynamical Model of Growth of Membership to an Opinion
Many social processes, from elections to terrorism, depend on growth of memberships to opinions. In a generic sense, an opinion is a proposition that for an individual has financial, cultural and emotional impli-cations. The individual responses in turn create a ‘social response’ which influences the individual response resulting in a dynamical system with two-way feed-backs. We consider a set of deterministic dynamical equations that describe individual response to a class of prescribed opinions. The time-dependent opinion dynamics model exhibits nearly complete acceptance to nearly complete rejection with complex evolution, providing the framework for a mechanistic descrip-tion of opinion formation.
Keywords
Dynamic Model, Growth of Membership, Opinion Dynamics, Social Engineering.
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- Jalili, M., Social power and opinion formation in complex networks. Phys. A, 2013, 392(4), 959–966.
- Hegselmann, R. and Flache, A., Understanding complex social dynamics – a plea for cellular automata based modelling. J. Art. Soci. Soc. Simul., 1998, 1.
- Li, P. P. and Hui, P. M., Dynamics of opinion formation in hierar-chical social networks: networks structure and initial bias. Eur. Phys. J.B, 2008, 61, 371–376.
- Toral R. and Tessone, C. J., Finite size effects in the dynamics of opinion formation. Commun. Comput. Phys., 2007, 2, 177–195.
- Wu, F. and Huberman, B., Social structure and opinion formation. Comput. Econ., 2004, 0407002.
- Moussaid, M., Kammer, J. E., Analytis, P. P. and Neth, H., Social influence and the collective dynamics of opinion formation. PLoS ONE, 2013, 8(11), e78433.
- Krause, U., A discrete nonlinear and non-autonomous model of consensus formation. In Communications in Difference Equations (eds Flaydi, S. et al.), Gordon and Breach Publication, Amster-dam, 2000, pp. 227–236.
- Shang, Y., Consensus formation of two-level opinion dynamics. Acta Math. Sci., 2014, 34(4), 1029–1040.
- Takao, F., A simple model of consensus formation. Okayama Econ. Rev., 1999, 31, 95–100.
- Galam, S., The dynamics of minority opinions in democratic debate. Phys. A, 2004, 336, 56–62.
- Laguna, M. F., Abramson, G. and Zanette, D., Minorities in a model for opinion formation. Complexity, 2004, 9(4), 31–36.
- Mogilner, A., Edelstein-Keshet, L., Bent, L. and Spiros, A., Mutual interactions, potentials, and individual distance in a social aggre-gation. J. Math. Biol., 2003, 47, 353–389.
- Mobilia, M. and Redner, S., Majority versus minority dynamics: phase transition in an interacting two-state spin system. Phys. Rev. E, 2003, 68(4), 046106.
- Boccara, N., Models of opinion formation: influence of opinion leaders. Int. J. Mod. Phys. C, 2008, 19, 93–109.
- Crespi, B. J., The evolution of social behaviour in micro-organisms. Trends Ecol. Evol., 2001, 16(4), 178–183.
- Wollman, N. P. et al., The dynamics of animal social networks: analytical, conceptual, and theoretical advances. Behav. Ecol., 2013, 25(2), 242–255.
- Ghosh, R. and Lerman, K., The impact of network flows on com-munity formation in models of opinion dynamics. J. Math. Soc., 2015, 39(2), 109–124.
- Hoylst, J. A., Kacperski, K. and Schweitzer, F., Social impact models of opinion dynamics. Ann. Rev. Comput. Phys., 2001, IX, 253–273.
- Antal, T., Krapivsky, P. L. and Redner, S., Dynamics of social balance on networks. Phys. Rev. E, 2005, 72, 036121.
- Altafini, C., Dynamics of opinion forming in structurally balanced social networks. PLoS ONE, 2012, 7(6), e38135.
- Gueron, S., Levin, S. A. and Rubenstein, D. I., The dynamics of herds: from individuals to aggregations. J. Theor. Biol., 1996, 182(1), 85–98.
- Fieldhouse, E., Shryane, N. and Pickles, A., Strategic voting and constituency context: modelling party preference and vote in multiparty elections. Polit. Geogr., 2007, 26(2), 159–178.
- Jiao, Y., Syau, Y. R. and Lee, E. S., Fuzzy adaptive network in presidential elections. Math. Comput. Model., 2006, 43, 244–253.
- Berger, R. L., A necessary and sufficient condition for reaching a consensus using DeGischolar_main’s method. J. Am. Stat. Assoc., 1981, 76(374), 415–418.
- Kosse, K., Group size and societal complexity: thresholds in the long-term memory. J. Anthropol. Archaeol., 1990, 9, 275–303.
- Farine, D. R. et al., The role of social and ecological processes in structuring animal populations: a case study from automated track-ing of wild birds. R. Soc. Open Sci., 2015, 2, 150057.
- Belenky, A. S. and King, D. C., A mathematical model for esti-mating the potential margin of state undecided voters for a candi-date in a US Federal election. Math. Comput. Model., 2007, 45, 585–593.
- Mishra, A. K., A simple mathematical model for the spread of two political parties. Nonlinear Anal. Model. Control, 2012, 17, 343–354.
- Farley, J. D., Evolutionary dynamics of the insurgency in Iraq: a mathematical model of the battle for hearts and minds. Stud. Confl. Terror., 2007, 30(11), 947–962.
- Anderton, C. H. and Carter, J. R., On rational choice theory and the study of terrorism. Def. Peace Econ., 2005, 16, 275–282.
- Facchetti, G., Iacono, G. and Altafini, C., Computing global struc-tural balance in large-scale signed social networks. Proc. Natl. Acad. Sci., 2011, 108(52), 20953–20958.
- Latane, B. and Nowak, A., Self-organizing social systems, neces-sary and sufficient conditions for the emergence of clustering, consolidation, and continuing diversity. In Progress in Communi-cation Science: Advances in Persuasion (eds Barnet, G. and Bostner, F.), Norwood, NJ, USA, Ablex Publishing Corporation, 1997, pp. 43–74.
- Iacono, G. and Altafini, C., Monotonicity, frustration, and ordered response: an analysis of the energy landscape of perturbed large-scale biological networks. BMC Syst. Biol., 2010, 4(1), 83.
- Weisbuch, G., Deffuant, G. and Amblard, F., Persuasion dynamics. Phys. A, 2005, 353, 555–575.
- Kawachi, K., Deterministic models for rumor transmission. Non-linear Anal. Real World Appl., 2008, 9, 1989–2028.
- Hegselmann, R. and Krause, U., Opinion dynamics and bounded confidence: models, analysis, and simulation. JASSS, 2002, 5(3), 1–33.
- Klir, G. J. and Yuan, B., Fuzzy Sets and Fuzzy Logic; Theory and Applications, Prentice Hall PTR, New Jersey, 1995.
- Cao, S., Dehmer, M. and Shi, Y., Extremality of degree-based graph entropies. Inf. Sci., 2014, 278, 22–33.
- Chen, Z., Dehmer, M., Emmert-Streib, F. and Shi, Y., Entropy of weighted graphs with Randi’c weights. Entropy, 2015, 17(6), 3710–3723.
- Chen, Z., Dehmer, M. and Shi, Y., A note on distance-based graph entropies. Entropy, 2014, 16(10), 5416–5427.
- Chen, Z., Dehmer, M. and Shi, Y., Bounds for degree-based network entropies. Appl. Math. Comput, 2015, 265, 983–993.
- Saganowski, S. et al., Predicting community evolution in social networks. Entropy, 2015, 17(5), 3053–3096.
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