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Motivated by various random variations of Hegselmann-Krause model for opinion dynamics and gossip algorithm in an endogenously changing environment, we propose a general framework for the study of endogenously varying random averaging…

Optimization and Control · Mathematics 2014-01-15 Behrouz Touri , Cedric Langbort

We extend a classical model of continuous opinion formation to explicitly include an age-structured population. We begin by considering a stochastic differential equation model which incorporates ageing dynamics and birth/death processes,…

Analysis of PDEs · Mathematics 2026-01-14 Andrew Nugent , Susana N. Gomes , Marie-Therese Wolfram

We study the Hegselmann-Krause model of opinion dynamics on sparse, unbiased networks generated via Wilson's algorithm, unveiling how network connectivity and confidence bounds jointly determine collective behavior. By systematically…

Physics and Society · Physics 2025-07-22 Paolo Molignini

Mechanistic and tractable mathematical models play a key role in understanding how social influence shapes public opinions. Recently, a weighted-median mechanism has been proposed as a new micro-foundation of opinion dynamics and validated…

Systems and Control · Electrical Eng. & Systems 2022-12-20 Wenjun Mei , Julien M. Hendrickx , Ge Chen , Francesco Bullo , Florian Dörfler

In this work, we derive a new upper bound on the termination time of the Hegselmann-Krause model for opinion dynamics. Using a novel method, we show that the termination rate of this dynamics happens no longer than $O(n^3)$ which improves…

Dynamical Systems · Mathematics 2012-11-20 Soheil Mohajer , Behrouz Touri

In the consensus model of Krause-Hegselmann, opinions are real numbers between 0 and 1 and two agents are compatible if the difference of their opinions is smaller than the confidence bound parameter \epsilon. A randomly chosen agent takes…

Statistical Mechanics · Physics 2009-11-10 Santo Fortunato

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…

Pattern Formation and Solitons · Physics 2017-04-28 Matt Holzer , Ratna Khatri

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

We consider a stochastic, continuous state and time opinion model where each agent's opinion locally interacts with other agents' opinions in the system, and there is also exogenous randomness. The interaction tends to create clusters of…

Social and Information Networks · Computer Science 2016-02-29 Josselin Garnier , George Papanicolaou , Tzu-Wei Yang

We study pattern formation in the bounded confidence model of opinion dynamics. In this random process, opinion is quantified by a single variable. Two agents may interact and reach a fair compromise, but only if their difference of opinion…

Pattern Formation and Solitons · Physics 2015-11-06 E. Ben-Naim , A. Scheel

With the analysis of noise-induced synchronization of opinion dynamics with bounded confidence (BC), a natural and fundamental question is what opinion structures can be synchronized by noise. In the traditional Hegselmann-Krause (HK)…

Systems and Control · Computer Science 2018-10-10 Wei Su , Ge Chen , Yongguang Yu , Xueqiao Wang

Stability and stabilization for linear state feedback control systems in the presence of sensor quantization are studied. As the closed-loop system is described by a discontinuous right-hand side differential equation, Krasovskii solutions…

Optimization and Control · Mathematics 2021-12-21 Francesco Ferrante , Frédéric Gouaisbaut , Sophie Tarbouriech

In this paper, we propose a new model for continuous time opinion dynamics on an evolving network. As opposed to existing models, in which the network typically evolves by discretely adding or removing edges, we instead propose a model for…

Physics and Society · Physics 2023-05-17 Andrew J. Nugent , Susana N. Gomes , Marie-Therese Wolfram

We introduce a utility-driven bounded-confidence model of opinion dynamics in which opinions associated with higher utility exert stronger social influence. In the regime where all agents belong to a single opinion cluster, we derive a…

Adaptation and Self-Organizing Systems · Physics 2026-05-22 Alex Siebenmorgen , Juan G. Restrepo

We study convergence of the following discrete-time non-linear dynamical system: n agents are located in R^d and at every time step, each moves synchronously to the average location of all agents within a unit distance of it. This popularly…

Data Structures and Algorithms · Computer Science 2012-11-09 Arnab Bhattacharyya , Mark Braverman , Bernard Chazelle , Huy L. Nguyen

We consider a certain class of nonlinear maps that preserve the probability simplex, i.e., stochastic maps, that are inspired by the DeGroot-Friedkin model of belief/opinion propagation over influence networks. The corresponding dynamical…

Systems and Control · Computer Science 2018-10-11 Zahra Askarzadeh , Rui Fu , Abhishek Halder , Yongxin Chen , Tryphon T. Georgiou

This paper introduces a class of non-linear and continuous-time opinion dynamics model with additive noise and state dependent interaction rates between agents. The model features interaction rates which are proportional to a negative power…

Probability · Mathematics 2020-12-15 Jae Oh Woo , François Baccelli , Sriram Vishwanath

In this work we study the coupled dynamics of social balance and opinion formation. We propose a model where agents form opinions under bounded confidence, but only considering the opinions of their friends. The signs of social ties…

Physics and Society · Physics 2016-10-11 Antonio Parravano , Ascención Andina-Díaz , Miguel A Meléndez-Jiménez

We review the opinion dynamics in the computer models of Deffuant et al. (D), of Krause and Hegselmann (KH), and of Sznajd (S). All these models allow for consensus (one final opinion), polarization (two final opinions), and fragmentation…

Disordered Systems and Neural Networks · Physics 2007-05-23 Santo Fortunato , Dietrich Stauffer

We study generalizations of the Hegselmann-Krause (HK) model for opinion dynamics, incorporating features and parameters that are natural components of observed social systems. The first generalization is one where the strength of influence…

Dynamical Systems · Mathematics 2014-09-29 Avhishek Chatterjee , Anand D. Sarwate , Sriram Vishwanath