Opinion Formation Systems via Deterministic Particles Approximation

Opinion formation process in a hierarchical society

In this work we study the formation of consensus in a hierarchical population. We derive the corresponding kinetic equations, and analyze the long time behaviour of their solutions for the case of finite number of hierarchical obtaining explicit formula for the consensus opinion.

Opinion formation models with heterogeneous persuasion and zealotry

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 other agent. In addition, our model includes zealots or stubborn agents, agents that never change opinions. We derive a Bolzmann-like equation for the distribution of agents on the space of opinions, which is approximated by a transport equation with a nonlocal drift term. We study the long-time asymptotic behavior of solutions, characterizing the limit distrib…

数学建模中的前向-前向平均场博弈及其在意见形成与投票模型中的应用

Forward-Forward Mean Field Games in mathematical modeling with application to opinion formation and voting models

本研究探讨前向-前向平均场博弈问题的适定性，论证其适用于建模掌握过往状态、不了解未来的参与者系统，并展示其在意见形成等社会现象数学建模中的应用价值。

具有连续年龄结构的意见动力学

Opinion Dynamics with Continuous Age Structure

本文提出了一种考虑连续年龄结构的意见动力学模型，通过随机微分方程和平均场偏微分方程分析意见形成过程，证明了稳态状态的存在并探讨了其与现有模型的联系。

Consensus of the Hegselmann-Krause opinion formation model with time delay

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 for this are based on Lyapunov functional approach and careful estimates on the trajectories. We then study the mean-field limit from the many-individual Hegselmann-Krause equation to the continuity-type partial differential equation as the number N of individuals goes to infinity. For the limiting equation, we prove global-in-time existence and uniqueness …

多维意见形成

Multi-Dimensional Opinion Formation

本文提出一种多维意见动力学模型，通过加权相似性机制描述意见变化，并展示意见结构由个体重要性权重决定。