Deffuant model of opinion formation in one-dimensional multiplex networks

Complex systems in the real world often operate through multiple kinds of links connecting their constituents. In this paper we propose an opinion formation model under bounded confidence over multiplex networks, consisting of edges at different topological and temporal scales. We determine rigorously the critical confidence threshold by exploiting probability theory and network science when the nodes are arranged on the integers, , evolving in continuous time. It is found that the existence of 'multiplexity' impedes the convergence, and that working with the aggregated or summarized simplex network is inaccurate since it misses vital information. Analytical calculations are confirmed by extensive numerical simulations.

[1]  Virgil D. Gligor,et al.  Analysis of complex contagions in random multiplex networks , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  S. Fortunato,et al.  Statistical physics of social dynamics , 2007, 0710.3256.

[3]  R. Durrett.  Probability: Theory and Examples , 1993 .

[4]  S. Galam.  Minority opinion spreading in random geometry , 2002, cond-mat/0203553.

[5]  Guido Caldarelli,et al.  Opinion dynamics on interacting networks: media competition and social influence , 2014, Scientific Reports.

[6]  Floriana Gargiulo,et al.  Opinion dynamics in a group-based society , 2010 .

[7]  Damon Centola,et al.  The Spread of Behavior in an Online Social Network Experiment , 2010, Science.

[8]  Evguenii V. Kurmyshev,et al.  Dynamics of bounded confidence opinion in heterogeneous social networks: concord against partial antagonism , 2011, ArXiv.

[9]  Yilun Shang,et al.  An agent based model for opinion dynamics with random confidence threshold , 2014, Commun. Nonlinear Sci. Numer. Simul..

[10]  Sergio Gómez,et al.  On the dynamical interplay between awareness and epidemic spreading in multiplex networks , 2013, Physical review letters.

[11]  Rainer Hegselmann,et al.  Opinion dynamics and bounded confidence: models, analysis and simulation , 2002, J. Artif. Soc. Soc. Simul..

[12]  Luis Mario Floría,et al.  Evolution of Cooperation in Multiplex Networks , 2012, Scientific Reports.

[13]  Katarzyna Sznajd-Weron,et al.  Opinion evolution in closed community , 2000, cond-mat/0101130.

[14]  Z. Wang,et al.  The structure and dynamics of multilayer networks , 2014, Physics Reports.

[15]  Further results on consensus formation in the Deffuant model , 2013, 1311.3223.

[16]  Harry Eugene Stanley,et al.  Catastrophic cascade of failures in interdependent networks , 2009, Nature.

[17]  H. Peyton Young,et al.  The dynamics of social innovation , 2011, Proceedings of the National Academy of Sciences.

[18]  A. Barrat,et al.  Consensus formation on adaptive networks. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[19]  Matthew O. Jackson,et al.  Does Homophily Predict Consensus Times? Testing a Model of Network Structure via a Dynamic Process , 2012 .

[20]  Guillaume Deffuant,et al.  Meet, discuss, and segregate! , 2002, Complex..

[21]  Jan Lorenz.  Consensus Strikes Back in the Hegselmann-Krause Model of Continuous Opinion Dynamics Under Bounded Confidence , 2006, J. Artif. Soc. Soc. Simul..

[22]  Ping Huang,et al.  Evolutionary Dynamics in Opinion Formation Model with Coupling of Social Communities , 2015, Adv. Complex Syst..

[23]  Alessandro Vespignani.  Modelling dynamical processes in complex socio-technical systems , 2011, Nature Physics.

[24]  K-I Goh,et al.  Multiplexity-facilitated cascades in networks. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[25]  N. Lanchier.  The critical value of the Deffuant model equals one half , 2012 .

[26]  S. Galam.  Heterogeneous beliefs, segregation, and extremism in the making of public opinions. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[27]  Yilun Shang.  Deffuant model with general opinion distributions: First impression and critical confidence bound , 2013, Complex..

[28]  S. Fortunato.  UNIVERSALITY OF THE THRESHOLD FOR COMPLETE CONSENSUS FOR THE OPINION DYNAMICS OF DEFFUANT et al , 2004, cond-mat/0406054.

[29]  K-I Goh,et al.  Threshold cascades with response heterogeneity in multiplex networks. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[30]  Sergio Gómez,et al.  Spectral properties of the Laplacian of multiplex networks , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[31]  Vito Latora,et al.  Structural measures for multiplex networks. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[32]  R. Huckfeldt,et al.  Political Disagreement: The Survival of Diverse Opinions within Communication Networks , 2004 .

[33]  P. Clifford,et al.  A model for spatial conflict , 1973 .

[34]  A Pairwise Averaging Procedure with Application to Consensus Formation in the Deffuant Model , 2012 .

[35]  Floriana Gargiulo,et al.  New Discussions Challenge the Organization of Societies , 2012, Adv. Complex Syst..

[36]  Yi Peng,et al.  Multi-Level Opinion Dynamics under Bounded Confidence , 2012, PloS one.

[37]  Yamir Moreno,et al.  Contact-based Social Contagion in Multiplex Networks , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[38]  U. Krause.  A DISCRETE NONLINEAR AND NON–AUTONOMOUS MODEL OF CONSENSUS FORMATION , 2007 .

[39]  Serge Galam,et al.  Local dynamics vs. social mechanisms: A unifying frame , 2005 .

[40]  Ljupco Kocarev,et al.  Discrete-time distributed consensus on multiplex networks , 2014 .

[41]  T. Liggett.  Interacting Particle Systems , 1985 .

[42]  Conrado J. Pérez Vicente,et al.  Diffusion dynamics on multiplex networks , 2012, Physical review letters.

[43]  Jan Lorenz,et al.  Continuous Opinion Dynamics under Bounded Confidence: A Survey , 2007, 0707.1762.

[44]  Guillaume Deffuant,et al.  Mixing beliefs among interacting agents , 2000, Adv. Complex Syst..

[45]  Peter Grindrod,et al.  A dynamical systems view of network centrality , 2014, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[46]  Yilun Shang,et al.  Consensus formation of two-level opinion dynamics , 2014 .

[47]  Jan Lorenz.  Heterogeneous bounds of confidence: Meet, discuss and find consensus! , 2010 .