Pattern formation, traveling fronts and consensus versus fragmentation in a model of opinion dynamics

Abstract

We consider a continuous version of the Hegselmann-Krause model of opinion dynamics. Interaction between agents either leads to a state of consensus, where agents converge to a single opinion as time evolves, or to a fragmented state with multiple opinions. In this work, we linearize the system about a uniform density solution and predict consensus or fragmentation based on properties of the resulting dispersion relation. This prediction is different depending on whether the initial agent distribution is uniform or nearly uniform. In the uniform case, we observe traveling fronts in the agent based model and make predictions for the speed and pattern selected by this front.

Noisy bounded confidence models for opinion dynamics: the effect of boundary conditions on phase transitions

“…Our first system has a uniform initial condition, which is standard in many opinion dynamics models, see, e.g. [28,55,47,27,31,67,34]. This initial condition is a steady state for both the periodic and even 2-periodic boundary conditions, which can be seen in Figure 1, and easily shown using the stationary PDE.…”

Opinion Dynamics with Higher-Order Bounded Confidence

“…A variety of mathematical tools have been used to investigate the properties of the bounded confidence model, by which the convergence [ 18 , 19 ], the pattern formation [ 20 ], the entropy [ 21 ], and the control theory [ 22 ] in the bounded confidence model have been studied. Other works focus on innovations in the model itself.…”

Opinion Dynamics with Higher-order Bounded Confidence

“…A variety of mathematical tools have been used to investigate the properties of the bounded confidence model, by which the convergence [17,18], the pattern formation [19], the entropy [20], and the control theory [21] in the bounded confidence model have been studied. Other works focus on innovations in the model itself.…”