{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,11]],"date-time":"2026-08-11T00:52:30Z","timestamp":1786409550319,"version":"build-2736575974"},"reference-count":27,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,1,17]],"date-time":"2023-01-17T00:00:00Z","timestamp":1673913600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>A discrete version of opinion dynamics systems, based on the Biswas\u2013Chatterjee\u2013Sen (BChS) model, has been studied on Barab\u00e1si\u2013Albert networks (BANs). In this model, depending on a pre-defined noise parameter, the mutual affinities can assign either positive or negative values. By employing extensive computer simulations with Monte Carlo algorithms, allied with finite-size scaling hypothesis, second-order phase transitions have been observed. The corresponding critical noise and the usual ratios of the critical exponents have been computed, in the thermodynamic limit, as a function of the average connectivity. The effective dimension of the system, defined through a hyper-scaling relation, is close to one, and it turns out to be connectivity-independent. The results also indicate that the discrete BChS model has a similar behavior on directed Barab\u00e1si\u2013Albert networks (DBANs), as well as on Erd\u00f6s\u2013R\u00e8nyi random graphs (ERRGs) and directed ERRGs random graphs (DERRGs). However, unlike the model on ERRGs and DERRGs, which has the same critical behavior for the average connectivity going to infinity, the model on BANs is in a different universality class to its DBANs counterpart in the whole range of the studied connectivities.<\/jats:p>","DOI":"10.3390\/e25020183","type":"journal-article","created":{"date-parts":[[2023,1,17]],"date-time":"2023-01-17T04:28:47Z","timestamp":1673929727000},"page":"183","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Opinion Dynamics Systems on Barab\u00e1si\u2013Albert Networks: Biswas\u2013Chatterjee\u2013Sen Model"],"prefix":"10.3390","volume":"25","author":[{"given":"David S. M.","family":"Alencar","sequence":"first","affiliation":[{"name":"Dietrich Stauffer Computational Physics Lab, Departamento de F\u00edsica, Universidade Federal do Piau\u00ed, Teresina 64049-550, PI, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tayroni F. A.","family":"Alves","sequence":"additional","affiliation":[{"name":"Dietrich Stauffer Computational Physics Lab, Departamento de F\u00edsica, Universidade Federal do Piau\u00ed, Teresina 64049-550, PI, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Gladstone A.","family":"Alves","sequence":"additional","affiliation":[{"name":"Departamento de F\u00edsica, Universidade Estadual do Piau\u00ed, Teresina 64002-150, PI, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Antonio","family":"Macedo-Filho","sequence":"additional","affiliation":[{"name":"Departamento de F\u00edsica, Universidade Estadual do Piau\u00ed, Teresina 64002-150, PI, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7623-1361","authenticated-orcid":false,"given":"Ronan S.","family":"Ferreira","sequence":"additional","affiliation":[{"name":"Departamento de Ci\u00eancias Exatas e Aplicadas, Universidade Federal de Ouro Preto, Jo\u00e3o Monlevade 35931-008, MG, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0895-4186","authenticated-orcid":false,"given":"F. Welington S.","family":"Lima","sequence":"additional","affiliation":[{"name":"Dietrich Stauffer Computational Physics Lab, Departamento de F\u00edsica, Universidade Federal do Piau\u00ed, Teresina 64049-550, PI, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5135-1674","authenticated-orcid":false,"given":"Joao A.","family":"Plascak","sequence":"additional","affiliation":[{"name":"Departamento de F\u00edsica, Centro de Ci\u00eancias Exatas e da Natureza, CCEN, Universidade Federal da Para\u00edba, Cidade Universit\u00e1ria, Jo\u00e3o Pessoa 58051-970, PB, Brazil"},{"name":"Departamento de F\u00edsica, Universidade Federal de Minas Gerais, C. 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