{"title":"具有状态依赖性的广义非线性模型在签名网络中的意见动态时标","authors":"","doi":"10.1016/j.jfranklin.2024.107313","DOIUrl":null,"url":null,"abstract":"<div><div>This article studies the opinions dynamics for a generalized nonlinear model with state-dependent susceptibility in signed networks on time scales. Unlike continuous-time or discrete-time models, time-scale systems can integrate continuous and discrete systems within a unified framework. Nevertheless, time-scale induced discontinuity properties can make it difficult to study the well-posedness and dynamics analysis of the opinions dynamics. In this paper, we first give a time-scale related condition to ensure the well-posedness of the nonlinear model. Then, based on time-scale theory, the comparison principle and the generalized Gronwall inequality, we focus on analyzing the dynamic behavior of the nonlinear model with three distinct susceptibility functions, which represent the behavior pattern of stubborn positives, stubborn extremists, and stubborn neutrals respectively. For the behavior pattern of stubborn positives and stubborn extremists, some sufficient conditions are given such that all agents’ viewpoints will converge exponentially towards a specific equilibrium point or achieve consensus under certain initial conditions. For the behavior pattern of stubborn neutrals, all agents’ opinions will finally reach neutrality.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":3.7000,"publicationDate":"2024-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Opinions dynamics for a generalized nonlinear model with state-dependent susceptibility in signed networks on time scales\",\"authors\":\"\",\"doi\":\"10.1016/j.jfranklin.2024.107313\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>This article studies the opinions dynamics for a generalized nonlinear model with state-dependent susceptibility in signed networks on time scales. Unlike continuous-time or discrete-time models, time-scale systems can integrate continuous and discrete systems within a unified framework. Nevertheless, time-scale induced discontinuity properties can make it difficult to study the well-posedness and dynamics analysis of the opinions dynamics. In this paper, we first give a time-scale related condition to ensure the well-posedness of the nonlinear model. Then, based on time-scale theory, the comparison principle and the generalized Gronwall inequality, we focus on analyzing the dynamic behavior of the nonlinear model with three distinct susceptibility functions, which represent the behavior pattern of stubborn positives, stubborn extremists, and stubborn neutrals respectively. For the behavior pattern of stubborn positives and stubborn extremists, some sufficient conditions are given such that all agents’ viewpoints will converge exponentially towards a specific equilibrium point or achieve consensus under certain initial conditions. For the behavior pattern of stubborn neutrals, all agents’ opinions will finally reach neutrality.</div></div>\",\"PeriodicalId\":17283,\"journal\":{\"name\":\"Journal of The Franklin Institute-engineering and Applied Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":3.7000,\"publicationDate\":\"2024-10-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of The Franklin Institute-engineering and Applied Mathematics\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0016003224007348\",\"RegionNum\":3,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"AUTOMATION & CONTROL SYSTEMS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of The Franklin Institute-engineering and Applied Mathematics","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0016003224007348","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
Opinions dynamics for a generalized nonlinear model with state-dependent susceptibility in signed networks on time scales
This article studies the opinions dynamics for a generalized nonlinear model with state-dependent susceptibility in signed networks on time scales. Unlike continuous-time or discrete-time models, time-scale systems can integrate continuous and discrete systems within a unified framework. Nevertheless, time-scale induced discontinuity properties can make it difficult to study the well-posedness and dynamics analysis of the opinions dynamics. In this paper, we first give a time-scale related condition to ensure the well-posedness of the nonlinear model. Then, based on time-scale theory, the comparison principle and the generalized Gronwall inequality, we focus on analyzing the dynamic behavior of the nonlinear model with three distinct susceptibility functions, which represent the behavior pattern of stubborn positives, stubborn extremists, and stubborn neutrals respectively. For the behavior pattern of stubborn positives and stubborn extremists, some sufficient conditions are given such that all agents’ viewpoints will converge exponentially towards a specific equilibrium point or achieve consensus under certain initial conditions. For the behavior pattern of stubborn neutrals, all agents’ opinions will finally reach neutrality.
期刊介绍:
The Journal of The Franklin Institute has an established reputation for publishing high-quality papers in the field of engineering and applied mathematics. Its current focus is on control systems, complex networks and dynamic systems, signal processing and communications and their applications. All submitted papers are peer-reviewed. The Journal will publish original research papers and research review papers of substance. Papers and special focus issues are judged upon possible lasting value, which has been and continues to be the strength of the Journal of The Franklin Institute.