Long-term Behavior of Mean-field Noisy Bounded Confidence Models with Distributed Radicals
M.A. Sharifi Kolarijani (TU Delft - Team Peyman Mohajerin Esfahani)
Anton V. Proskurnikov (Russian Academy of Sciences, Politecnico di Torino)
P. Mohajerin Mohajerinesfahani (TU Delft - Team Peyman Mohajerin Esfahani, TU Delft - Team Bart De Schutter)
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Abstract
In this paper, we consider the mean-field model of noisy bounded confidence opinion dynamics under exogenous influence of static radical opinions. The long-term behavior of the model is analyzed by providing a sufficient condition for exponential convergence of the dynamics to stationary state. The stationary state is also characterized by a global estimate for a sufficiently large noise. Furthermore, we consider the order-disorder transition in the model in order to identify the effect of the (relative) mass of the radicals on the critical noise level at which this transition occurs. A numerical scheme for approximating the critical noise level is provided and validated through numerical simulations of the mean-field model and the corresponding agent-based model for a particular distribution of radical opinions.