88 research outputs found
Macroscopic Noisy Bounded Confidence Models with Distributed Radical Opinions
In this article, we study the nonlinear Fokker-Planck (FP) equation that
arises as a mean-field (macroscopic) approximation of bounded confidence
opinion dynamics, where opinions are influenced by environmental noises and
opinions of radicals (stubborn individuals). The distribution of radical
opinions serves as an infinite-dimensional exogenous input to the FP equation,
visibly influencing the steady opinion profile. We establish mathematical
properties of the FP equation. In particular, we (i) show the well-posedness of
the dynamic equation, (ii) provide existence result accompanied by a
quantitative global estimate for the corresponding stationary solution, and
(iii) establish an explicit lower bound on the noise level that guarantees
exponential convergence of the dynamics to stationary state. Combining the
results in (ii) and (iii) readily yields the input-output stability of the
system for sufficiently large noises. Next, using Fourier analysis, the
structure of opinion clusters under the uniform initial distribution is
examined. Specifically, two numerical schemes for identification of
order-disorder transition and characterization of initial clustering behavior
are provided. The results of analysis are validated through several numerical
simulations of the continuum-agent model (partial differential equation) and
the corresponding discrete-agent model (interacting stochastic differential
equations) for a particular distribution of radicals
Multi-choice opinion dynamics model based on Latane theory
In this paper Nowak--Szamrej-Latan\'e model is reconsidered. This
computerised model of opinion formation bases on Latan\'e theory of social
impact. We modify this model to allow for multi (more than two) opinions. With
computer simulations we show that in the modified model the signatures of
order/disorder phase transition are still observed. The transition may be
observed in the average fraction of actors sharing the -th opinion, its
variation and also average number of clusters of actors with the same opinion
and the average size of the largest cluster of actors sharing the same opinion.
Also an influence of model control parameters on simulation results is shortly
reviewed. For a homogeneous society with identical actors' supportiveness and
persuasiveness the critical social temperature decreases with an increase
of available opinions from () via 4.7, 4.1 to for
, 4, 5, respectively.Comment: 12 page
Practical consensus in bounded confidence opinion dynamics
Abstract Opinion dynamics expressed by the bounded confidence discrete-time heterogeneous Hegselmann–Krause model is considered. A policy for the adaptation of the agents confidence thresholds based on heterophily, maximum number of neighbors and non-influencing similarity interval is proposed. The policy leads to the introduction of the concepts of practical clustering and practical consensus. Several properties of the agents dynamic behaviors are proved by exploiting the roles of the agents having at each time-step the maximum and the minimum opinions. The convergence in finite time to (a maximum number of) practical clusters and, for sufficiently large threshold bounds, the convergence to a practical consensus are proved. Sufficient conditions for reaching a practical consensus around a stubborn are derived too. Numerical simulations verify the theoretical results
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