2009/09/01 by Franco Bagnoli, Bagnoli, Franco, Graziano Barnabei +4
Physics and Astronomy · Social Sciences · #Complex Network Analysis Techniques #Evolutionary Game Theory and Cooperation #FOS: Physical sciences #Opinion Dynamics and Social Influence #Physics and Society (physics.soc-ph) #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.stat-mech #physics.soc-ph
paper · pdf · doi:10.48550/arxiv.0909.0117
11 pages, 4 figures
openalex publication_date 2009/09/01 · arxiv created 2009/12/23 · arxiv updated 2010/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study a cellular automaton opinion formation model of Ising type, with antiferromagnetic pair interactions modeling anticonformism, and ferromagnetic plaquette terms modeling the social norm constraints. For a sufficiently large connectivity, the mean-field equation for the average magnetization (opinion density) is chaotic. This "chaoticity" would imply irregular coherent oscillations of the whole society, that may eventually lead to a sudden jump into an absorbing state, if present. However, simulations on regular one-dimensional lattices show a different scenario: local patches may oscillate following the mean-field description, but these oscillations are not correlated spatially, so the average magnetization fluctuates around zero (average opinion near one half). The system is chaotic, but in a microscopic sense where local fluctuations tend to compensate each other. By varying the long-range rewiring of links, we trigger a small-world effect. We observe a bifurcation diagram for the magnetization, with period doubling cascades ending in a chaotic phase. As far as we know, this is the first observation of a small-world induced bifurcation diagram. The social implications of this transition are also interesting. In the presence of strong "anticonformistic" (or "antinorm") behavior, efforts for promoting social homogenization may trigger violent oscillations.