Analysis of an Opinion Dynamics Model Coupled with an External Environmental Dynamics

Chaos, Solitons & Fractals

Authors

Anthony Couthures

Vineeth Satheeskumar Varma

Samson Lasaulce

Irinel-Constantin Morărescu

Published

December 2024

Abstract
We consider a set of individuals, referred to as agents, whose opinions evolve according to nonlinear dynamics. Their opinions impact their behavior or actions, which in turn affect their local environment (for example, via pollution, contamination of a virus, etc.). Each agent can also perceive or observe a signal about the environment, and is influenced by this external signal. This yields a coupled dynamics (opinion and external signal), which behaves in a similar manner to the prey–predator models. One of the main features of our study is that the information provided by the external signal has a significant impact on the opinion dynamics. When the coupling is strong, the external signal may induce either chaotic behavior or convergence towards a limit cycle. When the coupling with the external signal is weak, the classical behavior characterized by local agreements in polarized clusters is observed. In both cases, conditions under which clusters of individuals do not change their actions are provided. Numerical examples are provided to illustrate the derived analytical results.

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Citation

BibTeX citation:
@article{couthures2024,
  author = {Couthures, Anthony and Satheeskumar Varma, Vineeth and
    Lasaulce, Samson and Morărescu, Irinel-Constantin},
  title = {Analysis of an {Opinion} {Dynamics} {Model} {Coupled} with an
    {External} {Environmental} {Dynamics}},
  journal = {Chaos, Solitons \& Fractals},
  volume = {189},
  pages = {115719},
  date = {2024-12},
  url = {https://anthonycouthures.github.io/publications/2024_csf_opinion-dynamics-external-environment.html},
  doi = {10.1016/j.chaos.2024.115719},
  langid = {en},
  abstract = {We consider a set of individuals, referred to as agents,
    whose opinions evolve according to nonlinear dynamics. Their
    opinions impact their behavior or actions, which in turn affect
    their local environment (for example, via pollution, contamination
    of a virus, etc.). Each agent can also perceive or observe a signal
    about the environment, and is influenced by this external signal.
    This yields a coupled dynamics (opinion and external signal), which
    behaves in a similar manner to the prey–predator models. One of the
    main features of our study is that the information provided by the
    external signal has a significant impact on the opinion dynamics.
    When the coupling is strong, the external signal may induce either
    chaotic behavior or convergence towards a limit cycle. When the
    coupling with the external signal is weak, the classical behavior
    characterized by local agreements in polarized clusters is observed.
    In both cases, conditions under which clusters of individuals do not
    change their actions are provided. Numerical examples are provided
    to illustrate the derived analytical results.}
}
For attribution, please cite this work as:
Anthony Couthures, Vineeth Satheeskumar Varma, Samson Lasaulce, and Irinel-Constantin Morărescu. 2024. “Analysis of an Opinion Dynamics Model Coupled with an External Environmental Dynamics.” Chaos, Solitons & Fractals 189: 115719. https://doi.org/10.1016/j.chaos.2024.115719.