Contrarian Voter Model under the influence of an Oscillating Propaganda: Consensus, Bimodal behavior and Stochastic Resonance

TL;DR

This paper investigates how external oscillating propaganda influences opinion dynamics in a contrarian voter model, revealing phase transitions, stochastic resonance, and the effects of social temperature on consensus and oscillatory behaviors.

Contribution

It introduces a model combining contrarian and imitation dynamics under periodic external influence, analyzing phase transitions and resonance phenomena with analytical and simulation methods.

Findings

Opinion consensus at zero temperature

Bimodal opinion distribution below critical temperature

Oscillatory behavior with maximum amplitude at intermediate temperature

Abstract

We study the contrarian voter model for opinion formation in a society under the influence of an external oscillating propaganda and stochastic noise. Each agent of the population can hold one of two possible opinions on a given issue --against or in favor, and interacts with its neighbors following either an imitation dynamics (voter behavior) or an anti-alignment dynamics (contrarian behavior): each agent adopts the opinion of a random neighbor with a time-dependent probability $p(t)$, or takes the opposite opinion with probability $1-p(t)$. The imitation probability $p(t)$ is controlled by the social temperature $T$, and varies in time according to a periodic field that mimics the influence of an external propaganda, so that a voter is more prone to adopt an opinion aligned with the field. We simulate the model in complete graph and in lattices, and find that the system exhibits a rich variety of behaviors as $T$ is varied: opinion consensus for $T=0$, a bimodal behavior for $T<T_c$, an oscillatory behavior where the mean opinion oscillates in time with the field for $T>T_c$, and full disorder for $T \gg 1$. The transition temperature $T_c$ vanishes with the population size $N$ as $T_c \simeq 2/\ln N$ in complete graph. Besides, the distribution of residence times $t_r$ in the bimodal phase decays approximately as $t_r^{-3/2}$. Within the oscillatory regime, we find a stochastic resonance-like phenomenon at a given temperature $T^*$. Also, mean-field analytical results show that the opinion oscillations reach a maximum amplitude at an intermediate temperature, and that exhibit a lag respect to the field that decreases with $T$.