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

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 (Formula presented.), or takes the opposite opinion with probability (Formula presented.). The imitation probability (Formula presented.) 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 (Formula presented.), a bimodal behavior for (Formula presented.), an oscillatory behavior where the mean opinion oscillates in time with the field for (Formula presented.), and full disorder for (Formula presented.). The transition temperature (Formula presented.) vanishes with the population size N as (Formula presented.) in complete graph. In addition, the distribution of residence times (Formula presented.) in the bimodal phase decays approximately as (Formula presented.). Within the oscillatory regime, we find a stochastic resonance-like phenomenon at a given temperature (Formula presented.). Furthermore, mean-field analytical results show that the opinion oscillations reach a maximum amplitude at an intermediate temperature, and that exhibit a lag with respect to the field that decreases with T.