Related papers: Hegselmann-Krause and Cucker-Smale type models wit…
We propose a large-scale scaling viewpoint for deriving mesoscopic dynamics from interacting particle systems and apply it to the Cucker--Smale flocking model. In contrast with the classical mean-field regime leading to the Vlasov-type…
One widely-existed state --``harmony with diversity" in which individuals freely express various viewpoints to sustain integration of social diversity, but at the same time shared values ensure social coherence, can be considered as the…
We study the convergence properties of Social Hegselmann-Krause dynamics, a {variant} of the Hegselmann-Krause (HK) model of opinion dynamics where a physical connectivity graph that accounts for the extrinsic factors that could prevent…
This paper focuses on the opinion dynamics under the influence of manipulative agents. This type of agents is characterized by the fact that their opinions follow a trajectory that does not respond to the dynamics of the model, although it…
This paper introduces a heterogeneous multidimensional bounded confidence (BC) opinion dynamics with random pairwise interactions, whereby each pair of agents accesses each other's opinions with a specific probability. This revised 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 a non-local two species cross-interaction model with cross-diffusion. We propose a positivity preserving finite volume scheme based on the numerical method introduced in Ref. [15] and explore this new model numerically in terms of…
In this paper, we model a decision-making process involving a set of interacting agents. We use Markovian opinion dynamics, where each agent switches between decisions according to a continuous time Markov chain. Existing opinion dynamics…
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…
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…
In this chapter, we present the Cucker-Smale type flocking models, and discuss their mathematical structures and flocking theorems in terms of coupling strength, interaction topologies and initial data. In 2007, two mathematicians Felipe…
We study the problem of consensus emergence in multi-agent systems via external feedback controllers. We consider a set of agents interacting with dynamics given by a Cucker-Smale type of model, and study its consensus stabilization by…
Within a simple model of attractive active Brownian particles, we predict flocking behavior and challenge the widespread idea that alignment interactions are necessary to observe this collective phenomenon. Here, we show that even…
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 -…
In this paper, we introduce the Iterative Persuasion-Polarization (IPP) model to study the dynamics of opinion formation and change within a population. The IPP model integrates mechanisms of persuasion and repulsion, where individuals…
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,…
We study multidimensional continuous opinion dynamics, where opinions are nonnegative vectors which components sum up to one. Examples of such opinions are budgets or other allocation vectors which display a distribution of a fixed amount…
We investigate a model for opinion dynamics, where individuals (modeled by vertices of a graph) hold certain abstract opinions. As time progresses, neighboring individuals interact with each other, and this interaction results in a…
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…
We investigate the long-time dynamics of an opinion formation model inspired by a work by Borghesi, Bouchaud and Jensen. Firstly, we derive a Fokker-Planck type equation under the assumption that interactions between individuals produce…