Abstract
This chapter is devoted to the analysis of some coevolving models for opinion formation that have been extensively studied in the literature. These models are grouped into two main classes: voter models and threshold models. The intrinsic dynamics of these models on static or very slowly varying topologies leads to coarsening and eventually to global order, if no interaction constraints are present. Moreover, the addition of some kind of link dynamics, in the form of removal or rewiring of connections, induces the appearance of new macroscopic patterns, such as stable or metastable coexistence of opinions, or the fragmentation of the network in communities.
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References
C. Castellano, S. Fortunato, V. Loreto, Statistical physics of social dynamics. Rev. Mod. Phys. 81, 591–646 (2009)
C. Cattuto, W. Van den Broeck, A. Barrat, V. Colizza, J.-F. Pinton, A. Vespignani, Dynamics of person-to-person interactions from distributed RFID sensor networks. PLoS ONE 5, e11596 (2010)
L. Isella, J. Stehlé, A. Barrat, C. Cattuto, J.-F. Pinton, W. Van den Broeck, What’s in a crowd? Analysis of face-to-face behavioral networks. J. Theor. Biol. 271, 166 (2011)
B. Latane, Pressure to uniformity and the evolution of cultural norms: Modeling dynamics of social impact, in Computational Modeling of Behavior in Organizations, ed. by C.L. Hulin, D.R. Illgen (American Psychological Association, Washington, DC, 2000), pp. 189–215
J.M. McPherson, L. Smith-Lovin, J. Cook, Birds of a feather: Homophily in social networks. Ann. Rev. Sociol. 27, 415–44 (2001)
D. Centola, An experimental study of homophily in the adoption of health behavior. Science 334, 1269 (2011)
T. Gross, B. Blasius, Adaptive coevolutionary networks: a review. J. R. Soc. Interface 5(20), 259–271 (2007)
T. Gross, H. Sayama (eds.), Adptive Networks: Theory, Models and Applications (Springer, New York, 2009)
S. Lozano, Dynamics of social complex networks: Some insights in recent research, in Dynamics On and Of Complex Networks: Aplications to Biology, Computer Science and the Social Sciences. Modeling and Simulation in Science, Engineering and Technology (Springer-Birkhauser), pp. 133–143 (2009)
D. Lazer, The co-evolution of individual and network. J. Math. Sociol. 25, 69–108 (2001)
T.M. Liggett, Interacting Particle Systems (Springer, New York, 1985)
M. Granovetter, Threshold models of collective behavior. Am. J. Sociol. 83(6), 1420 (1978)
M.E.J. Newman, Assortative mixing in networks. Phys. Rev. Lett. 89, 208701 (2002)
J. Stehlé, N. Voirin, A. Barrat, C. Cattuto, V. Colizza, L. Isella, C. Régis, J.-F. Pinton, N. Khanafer, W. Van den Broeck, P. Vanhems, Simulation of a SEIR infectious disease model on the dynamic contact network of conference attendees. BMC Med. 9, 87 (2011)
S.K. Maity, T.V. Manoj, A. Mukherjee, Opinion formation in time-varying social networks: The case of Naming Game, Phy. Rev. E 86, 036110 (2012)
P. Clifford, A. Sudbury, A model for spatial conflict. Biometrika 60(3), 581–588 (1973)
R.A. Holley, T.M. Liggett, Ergodic theorems for weakly interacting infinite systems and the voter model. Ann. Probab. 3, 643 (1975)
P.L. Krapivsky, Kinetics of monomer-monomer surface catalytic reactions. Phys. Rev. A 45, 1067 (1992)
L. Frachebourg, P.L. Krapivsky, Exact results for kinetics of catalytic reactions. Phys. Rev. E 53, R3009 (1996)
G.W. Gardiner, Handbook of Stochastic Methods (Springer-Verlang, Berlin), (1997)
F. Vazquez, C. Lopez, Systems with two symmetric absorbing states: relating the microscopic dynamics with the macroscopic behavior. Phys. Rev. E 78, 061127 (2008)
C. Castellano, D. Vilone, A. Vespignani, Incomplete ordering of the voter model on small-world networks. Europhys. Lett. 63, 153 (2003)
D. Vilone, C. Castellano, Solution of voter model dynamics on annealed small-world networks. Phys. Rev. E 69, 016109 (2004)
K. Suchecki, V.M. EguĂluz, M. San Miguel, Voter model dynamics in complex networks: Role of dimensionality, disorder, and degree distribution. Phys. Rev. E 72, 036132 (2005)
K. Suchecki, V.M. EguĂluz, M. San Miguel, Conservation laws for the voter model in complex networks. Europhys. Lett. 69, 228 (2005)
V. Sood, S. Redner, Voter model on heterogeneous graphs. Phys. Rev. Lett. 94, 178701 (2005)
V. Sood, T. Antal, S. Redner, Voter models on heterogeneous networks. Phys. Rev. E 77, 041121 (2008)
C. Castellano, V. Loreto, A. Barrat, F. Cecconi, D. Parisi, Comparison of voter and Glauber ordering dynamics on networks. Phys. Rev. E 71, 066107 (2005)
F. Vazquez, V.M. EguĂluz, Analytical solution of the voter model on uncorrelated networks. New J. Phys. 10, 063011 (2008)
D.H. Zanette, S. Gil, Opinion spreading and agent segregation on evolving networks. Phys. D 224, 156 (2006)
S. Gil, D.H. Zanette, Coevolution of agents and networks: Opinion spreading and community disconnection. Phys. Lett. A 356, 89 (2006)
P. Holme, M.E.J. Newman, Nonequilibrium phase transition in the coevolution of networks and opinions. Phys. Rev. E 74, 056108 (2006)
F. Vazquez, V.M. EguĂluz, M. San Miguel, Generic absorbing transition in coevolution dynamics. Phys. Rev. Lett. 100, 108702 (2008)
D. Kimura, Y. Hayakawa, Coevolutionary networks with homophily and heterophily. Phys. Rev. E 78, 016103 (2008)
C. Nardini, B. Kozma, A. Barrat, Who’s talking first? Consensus or lack thereof in coevolving opinion formation models. Phys. Rev. Lett. 100, 158701 (2008)
G. Demirel, R. Prizak, P.N. Reddy, T. Gross, Opinion formation and cyclic dominance in adaptive networks. Eur. Phys. J. B 84, 541–548 (2011)
B. Kozma, A. Barrat, Consensus formation on adaptive networks. Phys. Rev. E 77, 016102 (2008)
B. Kozma, A. Barrat, Consensus formation on coevolving networks: groups’ formation and structure. J. Phys. A Math. Theor. 41, 224020 (2008)
D. Centola, J.C. Gonzalez-Avella, V.M. Eguiluz, M. San Miguel, Homophily, cultural drift, and the co-evolution of cultural groups. J. Conflict Resolut. 51, 905–929 (2007)
F. Vazquez, J.C. González-Avella, V.M. EguĂluz, M. San Miguel, Time-scale competition leading to fragmentation and recombination transitions in the coevolution of network and states. Phys. Rev. E 76, 46120 (2007)
B. Wang, Y. Han, L. Chen, K. Aihara, Limited ability driven phase transitions in the coevolution process in Axelrod’s model. Phys. Lett. A 373, 1519 (2009)
C. Gracia-Lázaro, F. QuijandrĂa, L. Hernández, L.M. FlorĂa, Y. Moreno, Coevolutionary network approach to cultural dynamics controlled by intolerance. Phys. Rev. E 84, 067101 (2011)
S. Galam, Minority opinion spreading in random geometry. Eur. Phys. J. B 25, 403–406 (2002)
P.L. Krapivsky, S. Redner, Dynamics of majority rule in an interacting two-state spin system. Phys. Rev. Lett. 90, 238701 (2003)
P. Chen, S. Redner, Majority rule dynamics in finite dimensions. Phys. Rev. E 71, 036101 (2005)
R.J. Glauber, Time-dependent statistics of the ising model. J. Math. Phys. 4, 294 (1963)
V. Spirin, P.L. Krapivsky, S. Redner, Fate of zero-temperature ising ferromagnets. Phys. Rev. E 63, 036118 (2001)
V. Spirin, P.L. Krapivsky, S. Redner, Freezing in ising ferromagnets. Phys. Rev. E 65, 016119 (2001)
D. Boyer, O. Miramontes, Interface motion and pinning in small-world networks. Phys. Rev. E 67, 035102 (2003)
C. Castellano, R. Pastor-Satorras, Zero temperature Glauber dynamics on complex networks. J. Stat. Mech. P05001 (2006)
I.J. Benczik, S.Z. Benczik, B. Schmittmann, R.K.P. Zia, Lack of consensus in social systems. EPL 82, 48006 (2008)
I.J. Benczik, S.Z. Benczik, B. Schmittmann, R.K.P. Zia, Opinion dynamics on an adaptive random network. Phys. Rev. E 79, 046104 (2009)
R. Lambiotte, J.C. González-Avella, On co-evolution and the importance of initial conditions. Phys. A 390, 392–397 (2011)
F. Fu, L. Wang, Coevolutionary dynamics of opinions and networks: From diversity to uniformity. Phys. Rev. E 78, 016104 (2008)
S. Mandrà , S. Fortunato, C. Castellano, Coevolution of Glauber-like Ising dynamics and topology. Phys. Rev. E 80, 056105 (2009)
R. Pastor-Satorras, A. Vespignani, Epidemic spreading in scale-free networks. Phys. Rev. Lett. 86, 3200 (2001)
R. Pastor-Satorras, A. Vespignani, Epidemic dynamics and endemic states in complex networks. Phys. Rev. E 63, 066117 (2001)
Y. Moreno, R. Pastor-Satorras, A. Vespignani, Epidemic outbreaks in complex heterogeneous networks. Eur. Phys. J. B 26, 521 (2002)
E. Pugliese, C. Castellano, Heterogeneous pair approximation for voter models on networks. EPL 88, 58004 (2009)
P.-A. Noël, B. Davoudi, R.C. Brunham, L.J. Dubé, B. Pourbohloul, Time evolution of epidemic disease on finite and infinite networks. Phys. Rev. E 79, 026101 (2009)
V. Marceau, P.-A. Noël, L. Hébert-Dufresne, A. Allard, L.J. Dubé, Adaptive networks: Coevolution of disease and topology. Phys. Rev. E 82, 036116 (2010)
J.P. Gleeson, High-accuracy approximation of binary-state dynamics on networks. Phys. Rev. Lett. 107, 068701 (2011)
R. Durrett, J.P. Gleeson, A.L. Lloyd, P.J. Mucha, F. Shi, D. Sivakoff, J.E.S. Socolar, C. Varghese, Graph fission in an evolving voter model. Proc. Natl. Acad. Sci. USA 109, 3682–3687 (2012)
H. Matsuda, N. Ogita, A. Sasaki, K. Sato, Stochastical mechanics of population: The lattice Lotka-Volterra model. Prog. Theor. Phys. 88, 1035 (1992)
M.J. Keeling, The effects of local spatial structure on epidemiological invasions. Proc. R. Soc. Lond. B 266, 859 (1999)
R.K. Pathria, Statistical Mechanics (Butterworth-Heinemann), (1996)
H.E. Stanley, Introduction to Phase Transitions and Critical Phenomena (Oxford University Press, Oxford, 1971)
G.A. Böhme, T. Gross, Analytical calculation of fragmentation transitions in adaptive networks. Phys. Rev. E 83, 035101(R) (2011)
J.P. Gleeson, S. Melnik, J.A. Ward, M.A. Porter, P.J. Mucha, Accuracy of mean-field theory for dynamics on real-world networks. Phys. Rev. E 85, 026106 (2012)
M.S. Shkarayev, I.B. Schwartz, L.B. Shaw, Recruitment dynamics in adaptive social network, arXiv:1111.0964
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Vazquez, F. (2013). Opinion Dynamics on Coevolving Networks. In: Mukherjee, A., Choudhury, M., Peruani, F., Ganguly, N., Mitra, B. (eds) Dynamics On and Of Complex Networks, Volume 2. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser, New York, NY. https://doi.org/10.1007/978-1-4614-6729-8_5
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