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opinion dynamics; asymmetric Deffuant–Weisbuch model; convergence; separation time
In this paper, we investigate the convergence behavior of the asymmetric Deffuant-Weisbuch (DW) models during the opinion evolution. Based on the convergence of the asymmetric DW model that generalizes the conventional DW model, we first propose a new concept, the separation time, to study the transient behavior during the DW model's opinion evolution. Then we provide an upper bound of the expected separation time with the help of stochastic analysis. Finally, we show relations of the separation time with model parameters by simulations.
[1] Boyd, S., Ghosh, A., Prabhakar, B., Shah, D.: Randomized gossip algorithms. Trans. Inform. Theory 52 (2006), 2508-2530. DOI 10.1109/TIT.2006.874516 | MR 2238556 | Zbl 1283.94005
[2] Chow, Y., Teicher, H.: Probability Theory: Independence Interchangeability Martingales. Second edition. Springer-Verlag, Heidelberg - Berlin 1978. MR 0513230
[3] Deffuant, G., Neau, D., Amblard, F., Weisbuch, G.: Mixing beliefs among interacting agents. Adv. in Complex Systems 3 (2000), 87-98.
[4] Godsil, C., Royle, G.: Algebraic Graph Theory. Springer-Verlag, New York 2001. MR 1829620 | Zbl 0968.05002
[5] Groeber, P., Schweitzer, F., Press, K.: How groups can foster consensus: The case of local cultures. J. Artificial Societies and Social Simulations 12 (2009), 2/4.
[6] Harary, F.: A criterion for unanimity in French's theory of social power. In: Studies in Social Power, Ann Arbor 1959, pp. 168-182.
[7] Hegselmann, R., Krause, U.: Opinion dynamics and bounded confidence models. Analysis and Simulation. J. Artificial Societies and Social Simulations 5 (2002), 3.
[8] Hong, Y., Gao, L., Cheng, D., Hu, J.: Lyapuov-based approach to multi-agent systems with switching jointly connected interconnection. IEEE Trans. Automat. Control 52 (2007), 943-948. DOI 10.1109/TAC.2007.895860 | MR 2324260
[9] Hu, J.: On robust consensus of multi-agent systems with communication delays. Kybernetika 45 (2009), 768-784. MR 2599111 | Zbl 1190.93003
[10] Jiang, L., Hua, D., Zhu, J., Wang, B., Zhou., T.: Opinion dynamics on directed small-world networks. The European Physical Journal B 65 (2008), 2, 251-255. DOI 10.1140/epjb/e2008-00342-3
[11] Lorenz, J.: Continuous opinion dynamics under bounded confidence: A Survey. Internat. J. of Modern Physics C 18 (2007), 12, 1819-1838. DOI 10.1142/S0129183107011789 | Zbl 1151.91076
[12] Lou, Y., Hong, Y.: Target containment control of multi-agent systems with random switching interconnection topologies. Automatica 48 (2012), 5, 879-885. DOI 10.1016/j.automatica.2012.02.032 | MR 2912813 | Zbl 1246.93104
[13] Serge, M., Marisa, Z.: The group as a polarizer of attitudes. J. Personal. Soc. Psychology 12 (1969), 1, 125-135. DOI 10.1037/h0027568
[14] Shi, G., Hong, Y.: Global target aggregation and state agreement of nonlinear multi-agent systems with switching topologies. Automatica 45 (2009), 1165-1175. DOI 10.1016/j.automatica.2008.12.015 | MR 2531590 | Zbl 1162.93308
[15] Thunberg, J., Song, W., Hong, Y., Hu, X.: Distributed attitude synchronization using backstepping and sliding mode control. Journal of Control Theory and Applications 12 (2014), 1, 48-55. MR 3152182
[16] Touri, B.: Product of Random Stochastic Matrices And Distributed Averaging. Ph.D. Thesis, Dept. of Industrial Engineering in the Graduate College of the University of Illinois at Urbana-Champaign, 2011. Zbl 1244.15023
[17] Weisbuch, G., Deffuant, G., Amblard, F., Nadal, J.: Meet, discuss and segregate!. Complexity 7 (2002), 3, 55-63. DOI 10.1002/cplx.10031
[18] Zhang, J., Hong, Y.: Opinion evolution analysis for short-range and long-range Deffuant-Weisbuch models. Physica A 392 (2013), 5289-5297. DOI 10.1016/j.physa.2013.07.014 | MR 3102806
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