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

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: see text] , or takes the opposite opinion with probability [Formula: see text]. The imitation probability [Formula: see text] 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: see text] , a bimodal behavior for [Formula: see text] , an oscillatory behavior where the mean opinion oscillates in time with the field for [Formula: see text] , and full disorder for [Formula: see text]. The transition temperature [Formula: see text] vanishes with the population size N as [Formula: see text] in complete graph. In addition, the distribution of residence times [Formula: see text] in the bimodal phase decays approximately as [Formula: see text]. Within the oscillatory regime, we find a stochastic resonance-like phenomenon at a given temperature [Formula: see text]. 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.