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

2025 IEEE 64th Conference on Decision and Control (CDC)

Authors

Anthony Couthures

Anastasia Bizyaeva

Vineeth Satheeskumar Varma

Alessio Franci

Irinel-Constantin Morărescu

Published

December 2025

Abstract
We consider an opinion dynamics model coupled with an environmental dynamics. Based on a forward invariance argument, we can simplify the analysis of the asymptotic behavior to the case when all the opinions in the social network are synchronized. Our goal is to emphasize the role of the trust given to the environmental signal in the asymptotic behavior of the opinion dynamics and implicitly of the coupled system. To do that, we conduct a bifurcation analysis of the system around the origin when the trust parameter is varying. Specific conditions are presented for both pitchfork and Hopf bifurcation. Numerical illustration completes the theoretical findings.

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BibTeX citation:
@inproceedings{couthures2025,
  author = {Couthures, Anthony and Bizyaeva, Anastasia and Satheeskumar
    Varma, Vineeth and Franci, Alessio and Morărescu, Irinel-Constantin},
  title = {Bifurcation {Analysis} of an {Opinion} {Dynamics} {Model}
    {Coupled} with an {Environmental} {Dynamics}},
  booktitle = {2025 IEEE 64th Conference on Decision and Control (CDC)},
  pages = {3830-3835},
  date = {2025-12},
  url = {https://anthonycouthures.github.io/publications/2025_cdc_bifurcation-opinion-environment.html},
  doi = {10.1109/CDC57313.2025.11312255},
  langid = {en},
  abstract = {We consider an opinion dynamics model coupled with an
    environmental dynamics. Based on a forward invariance argument, we
    can simplify the analysis of the asymptotic behavior to the case
    when all the opinions in the social network are synchronized. Our
    goal is to emphasize the role of the trust given to the
    environmental signal in the asymptotic behavior of the opinion
    dynamics and implicitly of the coupled system. To do that, we
    conduct a bifurcation analysis of the system around the origin when
    the trust parameter is varying. Specific conditions are presented
    for both pitchfork and Hopf bifurcation. Numerical illustration
    completes the theoretical findings.}
}
For attribution, please cite this work as:
Anthony Couthures, Anastasia Bizyaeva, Vineeth Satheeskumar Varma, Alessio Franci, and Irinel-Constantin Morărescu. 2025. “Bifurcation Analysis of an Opinion Dynamics Model Coupled with an Environmental Dynamics.” 2025 IEEE 64th Conference on Decision and Control (CDC), 3830–3835. https://doi.org/10.1109/CDC57313.2025.11312255.