Year: 2024
Type: article
Abstract: 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 nongeneric 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.
Source: Physical review. E
Author: Gionni Marchetti
Institution: Universitat de Barcelona
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Award: G4772328477
OpenAlex ID: W4391591822