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We study a simple continuous-time multi-agent system related to Krause's model of opinion dynamics: each agent holds a real value, and this value is continuously attracted by every other value differing from it by less than 1, with an…

Optimization and Control · Mathematics 2009-07-28 Vincent D. Blondel , Julien M. Hendrickx , John N. Tsitsiklis

Memory effects play a crucial role in social interactions and decision-making processes. This paper proposes a novel fractional-order bounded confidence opinion dynamics model to characterize the memory effects in system states. Building…

Physics and Society · Physics 2025-06-06 Meiru Jiang , Wei Su , Guojian Ren , Yongguang Yu

This report studies a continuous-time version of the well-known Hegselmann-Krause model of opinion dynamics with bounded confidence. As the equations of this model have discontinuous right-hand side, we study their Krasovskii solutions. We…

Optimization and Control · Mathematics 2011-11-18 Francesca Ceragioli , Paolo Frasca

We study the optimal control problem of minimizing the convergence time in the discrete Hegselmann--Krause model of opinion dynamics. The underlying model is extended with a set of strategic agents that can freely place their opinion at…

Dynamical Systems · Mathematics 2015-04-28 Sascha Kurz

The consensus problem -- achieving agreement among a network of agents -- is a central theme in both theory and applications. Recently, this problem has been extended from Euclidean spaces to the space of probability measures, where the…

Optimization and Control · Mathematics 2025-10-01 Pilgyu Jung , Yoon Mo Jung

We study a time-delayed variant of the Hegselmann-Krause opinion formation model featuring a small group of leaders and a large group of non-leaders. In this model, leaders influence all agents but only interact among themselves. At the…

Analysis of PDEs · Mathematics 2026-03-31 Young-Pil Choi , Chiara Cicolani , Cristina Pignotti

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…

Optimization and Control · Mathematics 2025-06-16 Elisa Continelli , Cristina Pignotti

The original Deffuant model consists of a finite number of agents whose opinion is a number in $[0,1]$. Two socially connected agents are uniformly randomly selected at each time step and approach each other at a rate $\mu\in [0,1/2]$ if…

Probability · Mathematics 2021-12-07 Hsin-Lun Li

A stabilization theorem for processes of opinion dynamics is presented. The theorem is applicable to a wide class of models of continuous opinion dynamics based on averaging (like the models of Hegselmann-Krause and Weisbuch-Deffuant). The…

Physics and Society · Physics 2007-08-23 Jan Lorenz

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

We study a model of consensus decision making, in which a finite group of Bayesian agents has to choose between one of two courses of action. Each member of the group has a private and independent signal at his or her disposal, giving some…

Statistics Theory · Mathematics 2018-04-24 Elchanan Mossel , Omer Tamuz

We prove that asymptotic global consensus is always reached in the Hegselmann-Krause model with finite speed of information propagation $\mathfrak{c}>0$ under minimal (i.e., necessary) assumptions on the influence function. In particular,…

Analysis of PDEs · Mathematics 2023-03-14 Jan Haskovec , Mauro Rodriguez Cartabia

We study a continuous-time version of the Hegselmann-Krause model describing the opinion dynamics of interacting agents subject to random perturbations. Mathematically speaking, the opinion of agents is modelled by an interacting particle…

Probability · Mathematics 2024-11-25 Li Chen , Paul Nikolaev , David J. Prömel

In this paper we address the consensus problem in the context of networked agents whose communication graph can be split into a certain number of clusters in such a way that interactions between agents in the same clusters are cooperative,…

Systems and Control · Electrical Eng. & Systems 2020-08-31 Giulia De Pasquale , Maria Elena Valcher

A compromise process describes the evolution of opinions through binary interactions. Opinions are real numbers, and at each step, two randomly selected agents reach a compromise by averaging their pre-interaction opinions. We prove that if…

Physics and Society · Physics 2026-01-23 P. L. Krapivsky , A. Yu. Plakhov

This paper investigates some aspects of a recently proposed nonlinear mathematical model of opinion dynamics. The main objective is to identify the network structures that maximize the average equilibrium opinion (HMO). We prove that…

Optimization and Control · Mathematics 2025-09-19 David N. Reynolds , Pedro J. Torres

We study the Consensus problem among $n$ agents, defined as follows. Initially, each agent holds one of two possible opinions. The goal is to reach a consensus configuration in which every agent shares the same opinion. To this end, agents…

Distributed, Parallel, and Cluster Computing · Computer Science 2022-05-18 Petra Berenbrink , Amin Coja-Oghlan , Oliver Gebhard , Max Hahn-Klimroth , Dominik Kaaser , Malin Rau

We give an elementary proof of a conjecture by Hegselmann and Krause in opinion dynamics, concerning a symmetric bounded confidence interval model: If there is a truth and all individuals take each other seriously by a positive amount…

Dynamical Systems · Mathematics 2014-01-20 Sascha Kurz , Jörg Rambau

This work extends the recent opinion dynamics model from Cheng et al., emphasizing the role of group pressure in consensus formation. We generalize the findings to incorporate social influence algorithms with general time-varying,…

Physics and Society · Physics 2025-03-14 Iryna Zabarianska , Anton V. Proskurnikov

Eliminating disagreement in a group is usually beneficial to the social stability. In this paper, using the well-known Hegselmann-Krause (HK) model, we design a quite simple strategy that could resolve the opinion difference of the system…

Optimization and Control · Mathematics 2017-04-18 Wei Su , Ge Chen , Yongguang Yu