Bifurcation analysis of an opinion dynamics model coupled with an environmental dynamics
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866915228163244032 |
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| author | Couthures, Anthony Bizyaeva, Anastasia Varma, Vineeth S. Franci, Alessio Morarescu, Irinel-Constantin |
| author_facet | Couthures, Anthony Bizyaeva, Anastasia Varma, Vineeth S. Franci, Alessio Morarescu, Irinel-Constantin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_03419 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bifurcation analysis of an opinion dynamics model coupled with an environmental dynamics Couthures, Anthony Bizyaeva, Anastasia Varma, Vineeth S. Franci, Alessio Morarescu, Irinel-Constantin Systems and Control Dynamical Systems 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. |
| title | Bifurcation analysis of an opinion dynamics model coupled with an environmental dynamics |
| topic | Systems and Control Dynamical Systems |
| url | https://arxiv.org/abs/2504.03419 |