Related papers: How long does it take to consensus in the Hegselma…
A model for continuous-opinion dynamics is proposed and studied by taking advantage of its similarities with a mono-dimensional granular gas. Agents interact as in the Deffuant model, with a parameter $\alpha$ controlling the persuasibility…
Among the different disciplines in the social, behavioral and economic sciences, a fundamental class of problems is related to the prediction of the final state of the presence of individual opinions in a large population. The main aspects…
In this work an opinion formation model with heterogeneous agents is proposed. Each agent is supposed to have different power of persuasion, and besides its own level of zealotry, that is, an individual willingness to being convinced by…
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…
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…
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…
We present a model of opinion dynamics in which agents adjust continuous opinions as a result of random binary encounters whenever their difference in opinion is below a given threshold. High thresholds yield convergence of opinions towards…
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…
Unlike many complex networks studied in the literature, social networks rarely exhibit unanimous behavior, or consensus. This requires a development of mathematical models that are sufficiently simple to be examined and capture, at the same…
We reformulate the agent-based opinion dynamics models of Weisbuch-Deffuant and Hegselmann-Krause as interactive Markov chains. So we switch the scope from a finite number of n agents to a finite number of n opinion classes. Thus, we will…
We consider the problem of determining the existence of a sequence of matrices driving a discrete-time consensus system to consensus. We transform this problem into one of the existence of a product of the transition (stochastic) matrices…
Differences in opinion can be seen as distances between individuals, and such differences do not always vanish over time. In this paper, we propose a modeling framework that captures the formation of opinion clusters, based on extensions of…
This paper investigates the effect of constant time delay in weakly connected multi-agent systems modeled by double integrator dynamics. A novel analytical approach is proposed to establish an upper bound on the permissible time delay that…
We study a model of opinion formation where the collective decision of group is said to happen if the fraction of agents having the most common opinion exceeds a threshold value, a \textit{critical mass}. We find that there exists a unique,…
Formation of consensus, in binary yes/no type of voting, is a well defined process. However, even in presence of clear incentives, the dynamics involved can be incredibly complex. Specifically, formations of large groups of similarly…
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,…
Opinion dynamics is of paramount importance as it provides insights into the complex dynamics of opinion propagation and social relationship adjustment. It is assumed in most of the previous works that social relationships evolve much…
A new theorem on conditions for convergence to consensus of a multiagent time-dependent time-discrete dynamical system is presented. The theorem is build up on the notion of averaging maps. We compare this theorem to results by Moreau (IEEE…
Three conjectures from [R. Hegselmann, The Journal of Artificial Societies and Social Simulations 26(4), 11 (2023)] about the Hegselmann-Krause opinion dynamics and the structure of $\epsilon$-switches are proved. The first conjecture…
The behavior of one-dimensional Hegselmann-Krause (HK) dynamics driven by noise has been extensively studied. Previous research has indicated that within no matter the bounded or the unbounded space of one dimension, the HK dynamics attain…