{"title":"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","authors":"Simone Fagioli, Gianluca Favre","doi":"10.1017/s0956792524000093","DOIUrl":null,"url":null,"abstract":"\n 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.","PeriodicalId":51046,"journal":{"name":"European Journal of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.3000,"publicationDate":"2024-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Opinion formation on evolving network: the DPA method applied to a nonlocal cross-diffusion PDE-ODE system\",\"authors\":\"Simone Fagioli, Gianluca Favre\",\"doi\":\"10.1017/s0956792524000093\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"\\n 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.\",\"PeriodicalId\":51046,\"journal\":{\"name\":\"European Journal of Applied Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.3000,\"publicationDate\":\"2024-05-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"European Journal of Applied Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1017/s0956792524000093\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"European Journal of Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1017/s0956792524000093","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
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.
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.