相关论文: Consensus for the Hegselmann-Krause model with tim…
In this paper we study a Hegselmann-Krause opinion formation model with distributed time delay and positive influence functions. Through a Lyapunov functional approach, we provide a consensus result under a smallness assumption on the…
In this paper, we study Hegselmann-Krause models with a time-variable time delay. Under appropriate assumptions, we show the exponential asymptotic consensus when the time delay satisfies a suitable smallness assumption. Our main strategies…
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 Hegselmann-Krause type opinion formation models with non-universal interaction and time-delayed coupling. We assume the presence of a common influencer between two different agents. Moreover, we explore two cases in which such an…
We study a Hegselmann-Krause type opinion formation model for a system of two populations. The two groups interact with each other via subsets of individuals, namely the leaders, and natural time delay effects are considered. By using…
We analyze Hegselmann-Krause opinion formation models with leadership in presence of time delay effects. In particular, we consider a model with pointwise time variable time delay and a model with a distributed delay. In both cases we show…
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…
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,…
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…
We present a direct proof of asymptotic consensus in the nonlinear Hegselmann-Krause model with transmission-type delay, where the communication weights depend on the particle distance in phase space. Our approach is based on an explicit…
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 consensus model of Krause and Hegselmann can be naturally extended to the case in which opinions are integer instead of real numbers. Our algorithm is much faster than the original version and thus more suitable for applications. For…
The Hegselmann--Krause model is a prototypical model for opinion dynamics. It models the stochastic time evolution of an agent's or voter's opinion in response to the opinion of other like-minded agents. The Hegselmann--Krause model only…
Hegselmann and Krause introduced a discrete-time model of opinion dynamics with agents having limit confidence. It is well known that the dynamics reaches a stable state in a polynomial number of time steps. However, the gap between the…
We consider a variant of the Hegselmann-Krause model of consensus formation where information between agents propagates with a finite speed $\mathfrak{c}$. This leads to a system of ordinary differential equations (ODE) with state-dependent…
The aim of this paper is to provide a systematic overview of results on asymptotic consensus for the Hegselmann-Krause-type model with delay and discuss the corresponding analytical tools. We explain that two types (sources) of delay -…
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…
We present a simple proof of asymptotic consensus in the discrete Hegselmann-Krause model and flocking in the discrete Cucker-Smale model with renormalization and variable delay. It is based on convexity of the renormalized communication…
The original Hegselmann-Krause (HK) model comprises a set of $n$ agents characterized by their opinion, a number in $[0,1]$. Agent $i$ updates its opinion $x_i$ via taking the average opinion of its neighbors whose opinion differs by at…
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…