Journal
ENTROPY
Volume 24, Issue 8, Pages -Publisher
MDPI
DOI: 10.3390/e24081140
Keywords
opinion dynamics; voter model; noise; periodic field; stochastic resonance
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This study investigates the contrarian voter model for opinion formation, considering the impact of an external oscillating propaganda and stochastic noise. The results show that the social temperature plays a crucial role in determining the behavior of the system, leading to opinion consensus, bimodal behavior, oscillatory behavior, or full disorder. The study also observes the distribution of residence times and a stochastic resonance-like phenomenon at a certain temperature.
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 >> 1. The transition temperature T-c vanishes with the population size N as T-c similar or equal to 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.
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