Related papers: On the Convergence Properties of Social Hegselmann…
In opinion dynamics, the convergence of the heterogeneous Hegselmann-Krause (HK) dynamics has always been an open problem for years which looks forward to any essential progress. In this short note, we prove a partial convergence conclusion…
The mixed Hegselmann-Krause (HK) model covers the synchronous Hegselmann-Krause model, the asynchronous Hegselmann-Krause model and the Deffuant model. Previous study~\cite{mHK, mHK2} deals with the mixed HK model on finite graphs. In 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…
This paper presents a theoretical convergence analysis for an opinion-action coevolution model that integrates the opinion updating rule of the Hegselmann-Krause model with a utility-based decision-making mechanism. The model is…
The original Hegselmann-Krause (HK) model is composed of a finite number of agents characterized by their opinion, a number in $[0,1]$. An agent updates its opinion via taking the average opinion of its neighbors whose opinion differs by at…
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…
The Hegselmann-Krause (HK) model is a wellknown opinion dynamics, attracting a significant amount of interest from a number of fields. However, the heterogeneous HK model is difficult to analyze - even the most basic property of convergence…
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…
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…
Opinion spreading in a society decides the fate of elections, the success of products, and the impact of political or social movements. The model by Hegselmann and Krause is a well-known theoretical model to study such opinion formation…
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…
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…
This paper aims at providing rigorous theoretical analysis to investigate the consensus behavior of opinion dynamics in noisy environments. It is known that the well-known Hegselmann-Krause (HK) opinion dynamics demonstrates various…
We derive an energy bound for inertial Hegselmann-Krause (HK) systems, which we define as a variant of the classic HK model in which the agents can change their weights arbitrarily at each step. We use the bound to prove the convergence of…
The Hegselmann-Krause (HK) model allows one to characterize the continuous change of agents' opinions with the bounded confidence threshold $\varepsilon$. To consider the heterogeneity of agents in characteristics, we study the HK model on…
The Hegselmann-Krause (HK) model is a typical self-organizing system with local rule dynamics. In spite of its widespread use and numerous extensions, the underlying theory of its synchronization induced by noise still needs to be…
In opinion dynamics, how to model the enduring fragmentation phenomenon (disagreement, cleavage, and polarization) of social opinions has long possessed a central position. It is widely known that the confidence-based opinion dynamics…
The mixed Hegselmann-Krause (HK) model consists of a finite number of agents characterized by their opinion, a vector in $\mathbf{R^d}$. For the deterministic case, each agent updates its opinion by the rule: decide its degree of…
In this paper, we analyze a Hegselmann-Krause opinion formation model with attractive-lacking interaction. More precisely, we investigate the situation in which the individuals involved in an opinion formation process interact among…
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…