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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,…

Physics and Society · Physics 2008-03-06 Jan Lorenz

We present an extensive study of the joint effects of heterogeneous social agents and their heterogeneous social links in a bounded confidence opinion dynamics model. The full phase diagram of the model is explored for two different…

Physics and Society · Physics 2023-01-24 Rémi Perrier , Hendrik Schawe , Laura Hernández

Bounded confidence models of opinion dynamics have been actively studied in recent years, in particular, opinion formation and extremism propagation along with other aspects of social dynamics. In this work, after an analysis of limitations…

Physics and Society · Physics 2015-05-27 Evguenii Kurmyshev , Héctor A. Juárez , Ricardo A. González-Silva

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…

Optimization and Control · Mathematics 2024-12-05 Jiangjiang Cheng , Ge Chen , Wenjun Mei , Francesco Bullo

We perform a detailed study of the Hegselmann-Krause bounded confidence opinion dynamics model with heterogeneous confidence $\varepsilon_i$ drawn from uniform distributions in different intervals $[\varepsilon_l, \varepsilon_u]$. The phase…

Physics and Society · Physics 2020-05-22 Hendrik Schawe , Laura Hernández

This work focus on the effects of an external mass media on continuous opinion dynamics with heterogeneous bounds of confidence. We modified the original Deffuant et al. and Hegselmann and Krause models to incorporate both, an external mass…

Physics and Society · Physics 2014-11-21 M. Pineda , G. M. Buendia

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…

Physics and Society · Physics 2010-12-07 Jan Lorenz

Recently, significant attention has been dedicated to the models of opinion dynamics in which opinions are described by real numbers, and agents update their opinions synchronously by averaging their neighbors' opinions. The neighbors of…

Dynamical Systems · Mathematics 2011-04-08 Anahita Mirtabatabaei , Francesco Bullo

People's opinions on a wide range of topics often evolve over time through their interactions with others. Models of opinion dynamics primarily focus on one-dimensional opinions, which represent opinions on one topic. However, opinions on…

Physics and Society · Physics 2025-09-01 Grace Jingying Li , Jiajie Luo , Weiqi Chu

We study opinion dynamics over multiplex networks where agents interact with bounded confidence. Namely, two neighbouring individuals exchange opinions and compromise if their opinions do not differ by more than a given threshold. In…

Physics and Society · Physics 2018-01-30 Chris G. Antonopoulos , Yilun Shang

The bounded confidence model of opinion dynamics, introduced by Deffuant et al, is a stochastic model for the evolution of continuous-valued opinions within a finite group of peers. We prove that, as time goes to infinity, the opinions…

Probability · Mathematics 2011-04-19 Javier Gómez-Serrano , Carl Graham , Jean-Yves Le Boudec

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…

Mathematical Physics · Physics 2011-04-08 Anahita Mirtabatabaei , Francesco Bullo

Bounded confidence opinion dynamics model the propagation of information in social networks. However in the existing literature, opinions are only viewed as abstract quantities without semantics rather than as part of a decision-making…

Social and Information Networks · Computer Science 2015-06-17 Kush R. Varshney

The bounded confidence model represents a widely adopted framework for modeling opinion dynamics wherein actors have a continuous-valued opinion and interact and approach their positions in the opinion space only if their opinions are…

Physics and Society · Physics 2024-11-22 Irene Ferri , Emanuele Cozzo , Aleix Nicolas-Olive , Albert Diaz-Guilera , Luce Prignano

We study the continuum opinion dynamics of the compromise model of Krause and Hegselmann for a community of mutually interacting agents, by solving numerically a rate equation. The opinions are here represented by bidimensional vectors with…

Physics and Society · Physics 2009-11-11 Santo Fortunato , Vito Latora , Alessandro Pluchino , Andrea Rapisarda

In modern interconnected societies, opinions and beliefs can quickly spread across large populations, giving rise to collective behaviors such as the adoption of social norms or polarization. These phenomena have motivated many models aimed…

Physics and Society · Physics 2026-05-27 Cosimo Agostinelli , Marco Mancastroppa , Alain Barrat

Agent-based models of opinion dynamics allow one to examine the spread of opinions between entities and to study phenomena such as consensus, polarization, and fragmentation. By studying a model of opinion dynamics on a social network, one…

Physics and Society · Physics 2023-03-22 Grace J. Li , Mason A. Porter

We study the consensus formation for an agents based model, generalizing that originally proposed by Krause \cite{Kr}, by allowing the communication channels between any couple of agents to be switched on or off randomly, at each time step,…

Social and Information Networks · Computer Science 2026-03-26 Gianfelice Michele , Giuseppe Scola

People's opinions change with time as they interact with each other. In a bounded-confidence model (BCM) of opinion dynamics, individuals (which are represented by the nodes of a network) have continuous-valued opinions and are influenced…

Social and Information Networks · Computer Science 2024-07-30 Grace J. Li , Jiajie Luo , Mason A. Porter

We explore the possibilities of enforcing and preventing consensus in continuous opinion dynamics that result from modifications in the communication rules. We refer to the model of Weisbuch and Deffuant, where $n$ agents adjust their…

Physics and Society · Physics 2011-01-18 Jan Lorenz , Diemo Urbig
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