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| Format: | Preprint |
| Publié: |
2024
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| Accès en ligne: | https://arxiv.org/abs/2402.01940 |
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| _version_ | 1866916298441621504 |
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| author | Marchetti, Gionni |
| author_facet | Marchetti, Gionni |
| contents | We study the $β$-model ($β$-NG) and the Bayesian Naming Game (BNG) as dynamical systems. By applying linear stability analysis to the dynamical system associated with the $β$-model, we demonstrate the existence of a non-generic bifurcation with a bifurcation point $β_c = 1/3$. As $β$ passes through $β_c$, the stability of isolated fixed points changes, giving rise to a one-dimensional manifold of fixed points. Notably, this attracting invariant manifold forms an arc of an ellipse. In the context of the BNG, we propose modeling the Bayesian learning probabilities $p_A$ and $p_B$ as logistic functions. This modeling approach allows us to establish the existence of fixed points without relying on the overly strong assumption that $p_A = p_B = p$, where $p$ is a constant. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_01940 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generalized Naming Game and Bayesian Naming Game as Dynamical Systems Marchetti, Gionni Physics and Society We study the $β$-model ($β$-NG) and the Bayesian Naming Game (BNG) as dynamical systems. By applying linear stability analysis to the dynamical system associated with the $β$-model, we demonstrate the existence of a non-generic bifurcation with a bifurcation point $β_c = 1/3$. As $β$ passes through $β_c$, the stability of isolated fixed points changes, giving rise to a one-dimensional manifold of fixed points. Notably, this attracting invariant manifold forms an arc of an ellipse. In the context of the BNG, we propose modeling the Bayesian learning probabilities $p_A$ and $p_B$ as logistic functions. This modeling approach allows us to establish the existence of fixed points without relying on the overly strong assumption that $p_A = p_B = p$, where $p$ is a constant. |
| title | Generalized Naming Game and Bayesian Naming Game as Dynamical Systems |
| topic | Physics and Society |
| url | https://arxiv.org/abs/2402.01940 |