演化网络中的意见形成：应用于非局部交叉扩散 PDE-ODE 系统的 DPA 方法

IF 2.3 4区数学 Q1 MATHEMATICS, APPLIED

European Journal of Applied Mathematics Pub Date : 2024-05-21 DOI:10.1017/s0956792524000093

Simone Fagioli, Gianluca Favre

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引用次数: 0

摘要

我们研究了一个非局部聚集交叉扩散 PDEs 系统，该系统描述了网络上舆论密度的演变。该 PDEs 与描述网络上代理的时间演化的 ODEs 系统相耦合。首先，我们将确定性粒子逼近（DPA）方法应用于上述系统，以证明在代理之间相互作用的适当假设条件下，解的存在性。随后，我们提出了一个在不断演化的网络上形成意见的明确模型。意见的演变基于网络上代理之间的距离和 "态度区域"，而 "态度区域 "则取决于代理意见之间的距离。代理在网络中的位置根据代理意见之间的距离而变化。我们的目标是研究激进化、两极分化和人口分化，同时改变其思想开放程度和互动半径。

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Opinion formation on evolving network: the DPA method applied to a nonlocal cross-diffusion PDE-ODE system

We study a system of nonlocal aggregation cross-diffusion PDEs that describe the evolution of opinion densities on a network. The PDEs are coupled with a system of ODEs that describe the time evolution of the agents on the network. Firstly, we apply the Deterministic Particle Approximation (DPA) method to the aforementioned system in order to prove the existence of solutions under suitable assumptions on the interactions between agents. Later on, we present an explicit model for opinion formation on an evolving network. The opinions evolve based on both the distance between the agents on the network and the ’attitude areas’, which depend on the distance between the agents’ opinions. The position of the agents on the network evolves based on the distance between the agents’ opinions. The goal is to study radicalisation, polarisation and fragmentation of the population while changing its open-mindedness and the radius of interaction.

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来源期刊

European Journal of Applied Mathematics 数学-应用数学

CiteScore

4.70

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Since 2008 EJAM surveys have been expanded to cover Applied and Industrial Mathematics. Coverage of the journal has been strengthened in probabilistic applications, while still focusing on those areas of applied mathematics inspired by real-world applications, and at the same time fostering the development of theoretical methods with a broad range of applicability. Survey papers contain reviews of emerging areas of mathematics, either in core areas or with relevance to users in industry and other disciplines. Research papers may be in any area of applied mathematics, with special emphasis on new mathematical ideas, relevant to modelling and analysis in modern science and technology, and the development of interesting mathematical methods of wide applicability.