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

GIMENEZ, MARIA CECILIA; REINAUDI, LUIS; VAZQUEZ, FEDERICO

ENTROPY

MOLECULAR DIVERSITY PRESERVATION INTERNATIONAL-MDPI

Año: 2022 vol. 24

1099-4300

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 probabilityp ( 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 1. The transition temperature T c vanishes with the populationsize N as T c ´ 2/ ln N in complete graph. In addition, 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 ∗ . 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.