{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,14]],"date-time":"2026-04-14T22:24:13Z","timestamp":1776205453897,"version":"3.50.1"},"reference-count":57,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2022,8,17]],"date-time":"2022-08-17T00:00:00Z","timestamp":1660694400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Multidisciplinary Digital Publishing Institute (Switzerland)","award":["12345"],"award-info":[{"award-number":["12345"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>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\u2014against or in favor\u2014and 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\u2212p(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&lt;Tc, an oscillatory behavior where the mean opinion oscillates in time with the field for T&gt;Tc, and full disorder for T\u226b1. The transition temperature Tc vanishes with the population size N as Tc\u22432\/lnN in complete graph. In addition, the distribution of residence times tr in the bimodal phase decays approximately as tr\u22123\/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.<\/jats:p>","DOI":"10.3390\/e24081140","type":"journal-article","created":{"date-parts":[[2022,8,17]],"date-time":"2022-08-17T21:23:56Z","timestamp":1660771436000},"page":"1140","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Contrarian Voter Model under the Influence of an Oscillating Propaganda: Consensus, Bimodal Behavior and Stochastic Resonance"],"prefix":"10.3390","volume":"24","author":[{"given":"Maria Cecilia","family":"Gimenez","sequence":"first","affiliation":[{"name":"FaMAF (UNC), IFEG (CONICET), C\u00f3rdoba X5000HUA, Argentina"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9404-0753","authenticated-orcid":false,"given":"Luis","family":"Reinaudi","sequence":"additional","affiliation":[{"name":"Facultad de Ciencias Qu\u00edmicas (UNC), INFIQC (CONICET), C\u00f3rdoba X5000HUA, Argentina"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0773-5507","authenticated-orcid":false,"given":"Federico","family":"Vazquez","sequence":"additional","affiliation":[{"name":"Instituto de C\u00e1lculo, FCEyN, Universidad de Buenos Aires and Conicet, Intendente Guiraldes 2160, Cero + Infinito, Buenos Aires C1428EGA, Argentina"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,8,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"581","DOI":"10.1093\/biomet\/60.3.581","article-title":"A model for spatial conflict","volume":"60","author":"Clifford","year":"1973","journal-title":"Biometrika"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"643","DOI":"10.1214\/aop\/1176996306","article-title":"Ergodic Theorem for Weakly Interacting Infinite Systems and the voter model","volume":"3","author":"Holley","year":"1975","journal-title":"Ann. 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