意见模型中的小世界分歧
Smallworld bifurcations in an opinion model
摘要：
我们研究了一个元胞自动机的意见形成模型的伊辛型，反铁磁对相互作用建模的反从众，和铁磁plaquette项建模的社会规范的约束。对于足够大的连通性，平均磁化强度（意见密度）的平均场方程是混沌的。这种“混沌性”意味着整个社会的不规则连贯振荡，如果存在的话，最终可能导致突然跳跃到吸收状态。然而，对规则一维晶格的模拟显示了不同的情况：局部补丁可能会振荡的平均场的描述，但这些振荡是不相关的空间，所以平均磁化波动在零附近（平均意见接近一半）。系统是混沌的，但在微观意义上，局部波动往往相互补偿。通过改变链接的长距离重新布线，我们触发了小世界效应。我们观察到的磁化分岔图，倍周期级联结束于一个混乱的阶段。据我们所知，这是第一次观察到小世界诱导分岔图。这种转变的社会影响也很有趣。在强烈的“反墨守成规”（或“反正统”）行为的存在下，促进社会同质化的努力可能会引发剧烈的振荡。
英文摘要：
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.
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