Related papers: Robust Fragmentation Modeling of Hegselmann-Krause…
This paper introduces a heterogeneous multidimensional bounded confidence (BC) opinion dynamics with random pairwise interactions, whereby each pair of agents accesses each other's opinions with a specific probability. This revised model is…
In this paper, we analyze a Hegselmann-Krause opinion formation model with time-variable time delay and prove that, if the influence function is always positive, then there is exponential convergence to consensus without requiring any…
This paper is concerned with the probability of consensus in a multivariate, spatially explicit version of the Hegselmann-Krause model for the dynamics of opinions. Individuals are located on the vertices of a finite connected graph…
We study multidimensional continuous opinion dynamics, where opinions are nonnegative vectors which components sum up to one. Examples of such opinions are budgets or other allocation vectors which display a distribution of a fixed amount…
In this paper, we study Hegselmann-Krause models with a time-variable time delay. Under appropriate assumptions, we show the exponential asymptotic consensus when the time delay satisfies a suitable smallness assumption. Our main strategies…
In this paper, we analyze a Hegselmann-Krause opinion formation model and a Cucker-Smale flocking model with attractive-repulsive interaction. To be precise, we investigate the situation in which the individuals involved in an opinion…
Hegselmann and Krause introduced a discrete-time model of opinion dynamics with agents having limit confidence. It is well known that the dynamics reaches a stable state in a polynomial number of time steps. However, the gap between the…
We consider the Hegselmann-Krause model for opinion dynamics and study the evolution of the system under various settings. We first analyze the termination time of the synchronous Hegselmann-Krause dynamics in arbitrary finite dimensions…
In this paper we study a Hegselmann-Krause opinion formation model with distributed time delay and positive influence functions. Through a Lyapunov functional approach, we provide a consensus result under a smallness assumption on the…
This paper studies the opinion dynamics model recently introduced by Hegselmann and Krause: each agent in a group maintains a real number describing its opinion; and each agent updates its opinion by averaging all other opinions that are…
We consider a variant of the Hegselmann-Krause model of consensus formation where information between agents propagates with a finite speed $\mathfrak{c}$. This leads to a system of ordinary differential equations (ODE) with state-dependent…
We study damage spreading among the opinions of a system of agents, subjected to the dynamics of the Krause-Hegselmann consensus model. The damage consists in a sharp change of the opinion of one or more agents in the initial random opinion…
In a 2006 paper, Jan Lorenz observed a curious behaviour in numerical simulations of the Hegselmann-Krause model: Under some circumstances, making agents more closed-minded can produce a consensus from a dense configuration of opinions…
This paper elaborates control strategies to prevent clustering effects in opinion formation models. This is the exact opposite of numerous situations encountered in the literature where, on the contrary, one seeks controls promoting…
The arise of disagreement is an emergent phenomenon that can be observed within a growing social group and, beyond a certain threshold, can lead to group fragmentation. To better understand how disagreement emerges, we introduce an…
The rapid proliferation of social media as a dominant channel for information dissemination has intensified concerns over systemic information distortion, whereby content is progressively altered through successive layers of transmission.…
We consider the Hegselmann-Krause bounded confidence dynamics for n equally spaced opinions on the real line, with gaps equal to the confidence bound r, which we take to be 1. We prove rigorous results on the evolution of this…
This paper introduces a new model of continuous opinion dynamics with random noise. The model belongs to the broad class of so called bounded confidence models. It differs from other popular bounded confidence models by the update rule,…
We present two models of continuous opinion dynamics under bounded confidence which are representable as nonnegative discrete dynamical systems, namely the Hegselmann-Krause model (Hegselmann and Krause, Journal of Artificial Societies and…
Models of continuous opinion dynamics under bounded confidence have been presented independently by Krause and Hegselmann and by Deffuant et al in 2000. They have raised a fair amount of attention in the communities of social simulation,…