Research Article
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Dynamics of Indoctrination in Small Groups around Three Options

Year 2022, Volume 4, Issue 4, 241 - 245, 31.12.2022
https://doi.org/10.51537/chaos.1190234

Abstract

In this work, we consider the dynamics of opinion among three parties: two small groups of agents and one very persuasive agent, the indoctrinator. Each party holds a position different from that of the others. In this situation, the opinion space is required to be a circle, on which the agents express their position regarding three different options. Initially, each group supports a unique position, and the indoctrinator tries to convince them to adopt her or his position. The interaction between the agents is in pairs and is modeled through a system of non-linear difference equations. Agents, in both groups, give a high weight to the opinion of the indoctrinator, while they give the same weight to the opinion of their peers. Through several computational experiments, we investigate the times required by the indoctrinator to convince both groups.

References

  • Boccaletti, S., A. N. Pisarchik, C. I. Del Genio, and A. Amann, 2018 Synchronization: from coupled systems to complex networks. Cambridge University Press.
  • Caponigro, M., Lai, A. C., & Piccoli, B. (2015). A nonlinear model of opinion formation on the sphere. Discrete & Continuous Dynamical Systems, 35(9), 4241.
  • Dong, Y., Zhan, M., Kou, G., Ding, Z., & Liang, H. (2018). A survey on the fusion process in opinion dynamics. Information Fusion, 43, 57-65.
  • Hegarty, P., Martinsson, A., & Wedin, E. (2016). The Hegselmann-Krause dynamics on the circle converge. Journal of Difference Equations and Applications, 22(11), 1720-1731.
  • Medina-Guevara, M. G., Macías-Díaz, J. E., Gallegos, A., & Vargas-Rodríguez, H. (2017). On S1 as an alternative continuous opinion space in a three-party regime. Journal of Computational and Applied Mathematics, 318, 230-241.
  • Medina‐Guevara, M. G., Vargas‐Rodríguez, H., & Espinoza‐Padilla, P. B. (2019). (CMMSE paper) A finite‐difference model for indoctrination dynamics. Mathematical Methods in the Applied Sciences, 42(17), 5696-5707.
  • Medina Guevara, M. G., Vargas Rodríguez, H., Espinoza Padilla, P. B., & Gozález Solís, J. L. (2018). Evolution of electoral preferences for a regime of three political parties. Discrete Dynamics in Nature and Society, 2018.
  • Noorazar, H., Vixie, K. R., Talebanpour, A., & Hu, Y. (2020). From classical to modern opinion dynamics. International Journal of Modern Physics C, 31(07), 2050101.
  • Zha, Q., Kou, G., Zhang, H., Liang, H., Chen, X., Li, C. C., & Dong, Y. (2020). Opinion dynamics in finance and business: a literature review and research opportunities. Financial Innovation, 6(1), 1-22.
  • Zhang, Z., Al-Abri, S., & Zhang, F. (2021, December). Dissensus Algorithms for Opinion Dynamics on the Sphere. In 2021 60th IEEE Conference on Decision and Control (CDC) (pp. 5988-5993). IEEE.
  • Zhang, Z., Al-Abri, S., & Zhang, F. (2022). Opinion Dynamics on the Sphere for Stable Consensus and Stable Bipartite Dissensus. IFAC-PapersOnLine, 55(13), 288-293.

Year 2022, Volume 4, Issue 4, 241 - 245, 31.12.2022
https://doi.org/10.51537/chaos.1190234

Abstract

References

  • Boccaletti, S., A. N. Pisarchik, C. I. Del Genio, and A. Amann, 2018 Synchronization: from coupled systems to complex networks. Cambridge University Press.
  • Caponigro, M., Lai, A. C., & Piccoli, B. (2015). A nonlinear model of opinion formation on the sphere. Discrete & Continuous Dynamical Systems, 35(9), 4241.
  • Dong, Y., Zhan, M., Kou, G., Ding, Z., & Liang, H. (2018). A survey on the fusion process in opinion dynamics. Information Fusion, 43, 57-65.
  • Hegarty, P., Martinsson, A., & Wedin, E. (2016). The Hegselmann-Krause dynamics on the circle converge. Journal of Difference Equations and Applications, 22(11), 1720-1731.
  • Medina-Guevara, M. G., Macías-Díaz, J. E., Gallegos, A., & Vargas-Rodríguez, H. (2017). On S1 as an alternative continuous opinion space in a three-party regime. Journal of Computational and Applied Mathematics, 318, 230-241.
  • Medina‐Guevara, M. G., Vargas‐Rodríguez, H., & Espinoza‐Padilla, P. B. (2019). (CMMSE paper) A finite‐difference model for indoctrination dynamics. Mathematical Methods in the Applied Sciences, 42(17), 5696-5707.
  • Medina Guevara, M. G., Vargas Rodríguez, H., Espinoza Padilla, P. B., & Gozález Solís, J. L. (2018). Evolution of electoral preferences for a regime of three political parties. Discrete Dynamics in Nature and Society, 2018.
  • Noorazar, H., Vixie, K. R., Talebanpour, A., & Hu, Y. (2020). From classical to modern opinion dynamics. International Journal of Modern Physics C, 31(07), 2050101.
  • Zha, Q., Kou, G., Zhang, H., Liang, H., Chen, X., Li, C. C., & Dong, Y. (2020). Opinion dynamics in finance and business: a literature review and research opportunities. Financial Innovation, 6(1), 1-22.
  • Zhang, Z., Al-Abri, S., & Zhang, F. (2021, December). Dissensus Algorithms for Opinion Dynamics on the Sphere. In 2021 60th IEEE Conference on Decision and Control (CDC) (pp. 5988-5993). IEEE.
  • Zhang, Z., Al-Abri, S., & Zhang, F. (2022). Opinion Dynamics on the Sphere for Stable Consensus and Stable Bipartite Dissensus. IFAC-PapersOnLine, 55(13), 288-293.

Details

Primary Language English
Subjects Mathematics, Interdisciplinary Applications
Journal Section Research Articles
Authors

María Guadalupe MEDİNA GUEVARA This is me
University of Guadalajara
0000-0002-5381-8397
Mexico


Kurmyshev EVGUENİİ This is me
University of Guadalajara
0000-0003-2832-5918
Mexico


Hector VARGAS RODRİGUEZ> (Primary Author)
University of Guadalajara
0000-0003-1973-9852
Mexico

Supporting Institution No supporting Institution
Publication Date December 31, 2022
Published in Issue Year 2022, Volume 4, Issue 4

Cite

APA Medina Guevara, M. G. , Evguenii, K. & Vargas Rodriguez, H. (2022). Dynamics of Indoctrination in Small Groups around Three Options . Chaos Theory and Applications , Dissemination and Research in the Study of Complex Systems and Their Applications (EDIESCA 2022) , 241-245 . DOI: 10.51537/chaos.1190234

Chaos Theory and Applications in Applied Sciences and Engineering: An interdisciplinary journal of nonlinear science 23830