Smallworld bifurcations in an opinion model

TL;DR

This paper investigates how small-world network structures induce bifurcations and chaos in an opinion formation model, revealing complex social dynamics and potential oscillations in collective opinions.

Contribution

It demonstrates the first observation of small-world effects causing bifurcation diagrams in an opinion model with social norm constraints.

Findings

Small-world rewiring induces bifurcation cascades in opinion dynamics.

Chaotic oscillations can emerge from social norm and anticonformism interactions.

Local patches oscillate without global consensus, leading to fluctuating average opinions.

Abstract

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.