Bifurcations in models of a society of reasonable contrarians and conformists

TL;DR

This paper investigates how mixed populations of conformists and reasonable contrarians influence societal opinion dynamics, revealing bifurcations, polarization, and chaotic oscillations through mean field and network models.

Contribution

It introduces a novel model combining conformist and reasonable contrarian behaviors and analyzes bifurcations and complex dynamics on different network structures.

Findings

Large conformist fractions cause opinion polarization.

Majority of contrarians induce oscillatory behavior.

Network topology affects bifurcation patterns.

Abstract

We study models of a society composed of a mixture of conformist and reasonable contrarian agents that at any instant hold one of two opinions. Conformists tend to agree with the average opinion of their neighbors and reasonable contrarians to disagree, but revert to a conformist behavior in the presence of an overwhelming majority, in line with psychological experiments. The model is studied in the mean field approximation and on small-world and scale-free networks. In the mean field approximation, a large fraction of conformists triggers a polarization of the opinions, a pitchfork bifurcation, while a majority of reasonable contrarians leads to coherent oscillations, with an alternation of period-doubling and pitchfork bifurcations up to chaos. Similar scenarios are obtained by changing the fraction of long-range rewiring and the parameter of scale-free networks related to the average connectivity.