{"title":"Opinion dynamics analysis for stubborn individuals in cooperation–competition networks based on path-dependence framework","authors":"","doi":"10.1016/j.automatica.2024.111840","DOIUrl":null,"url":null,"abstract":"<div><p>The opinion evolution problem is studied in this paper for stubborn individuals in cooperation–competition networks, where the individuals’ opinion dynamics is described by the Friedkin–Johnsen model and the competitive relationship between individuals is characterized by negative weights. Then the lifting approach is successfully applied to the Friedkin–Johnsen model to deal with the influence of the negative weights while the path-dependence theory is used to the transition of two arbitrarily adjacent topics. Starting from the weight topology, the relationship between the weight topology and the augmented topology is established, and some sufficient conditions about achieving neutrality, bipartite consensus and convergence for the individuals’ opinions in a sequence of topics are obtained. Interestingly, a necessary and sufficient condition is given to ensure bipartite consensus for the individuals’ opinions under the premise that the weight topology is structurally unbalanced. Furthermore, the Friedkin–Johnsen model with dynamic stubbornness is also considered, and the concept of common topic subsequence is introduced. It is proved that all elements of the topic transfer matrix are positive for the common topic subsequence, and neutrality and bipartite consensus for the individuals’ opinions can be achieved for different types of weight topologies, respectively. Finally, numerical examples are given to support the correctness of the theoretical results.</p></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":null,"pages":null},"PeriodicalIF":4.8000,"publicationDate":"2024-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0005109824003340/pdfft?md5=5f98933c266fca464e87f52c41f5c094&pid=1-s2.0-S0005109824003340-main.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Automatica","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0005109824003340","RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
引用次数: 0
Abstract
The opinion evolution problem is studied in this paper for stubborn individuals in cooperation–competition networks, where the individuals’ opinion dynamics is described by the Friedkin–Johnsen model and the competitive relationship between individuals is characterized by negative weights. Then the lifting approach is successfully applied to the Friedkin–Johnsen model to deal with the influence of the negative weights while the path-dependence theory is used to the transition of two arbitrarily adjacent topics. Starting from the weight topology, the relationship between the weight topology and the augmented topology is established, and some sufficient conditions about achieving neutrality, bipartite consensus and convergence for the individuals’ opinions in a sequence of topics are obtained. Interestingly, a necessary and sufficient condition is given to ensure bipartite consensus for the individuals’ opinions under the premise that the weight topology is structurally unbalanced. Furthermore, the Friedkin–Johnsen model with dynamic stubbornness is also considered, and the concept of common topic subsequence is introduced. It is proved that all elements of the topic transfer matrix are positive for the common topic subsequence, and neutrality and bipartite consensus for the individuals’ opinions can be achieved for different types of weight topologies, respectively. Finally, numerical examples are given to support the correctness of the theoretical results.
期刊介绍:
Automatica is a leading archival publication in the field of systems and control. The field encompasses today a broad set of areas and topics, and is thriving not only within itself but also in terms of its impact on other fields, such as communications, computers, biology, energy and economics. Since its inception in 1963, Automatica has kept abreast with the evolution of the field over the years, and has emerged as a leading publication driving the trends in the field.
After being founded in 1963, Automatica became a journal of the International Federation of Automatic Control (IFAC) in 1969. It features a characteristic blend of theoretical and applied papers of archival, lasting value, reporting cutting edge research results by authors across the globe. It features articles in distinct categories, including regular, brief and survey papers, technical communiqués, correspondence items, as well as reviews on published books of interest to the readership. It occasionally publishes special issues on emerging new topics or established mature topics of interest to a broad audience.
Automatica solicits original high-quality contributions in all the categories listed above, and in all areas of systems and control interpreted in a broad sense and evolving constantly. They may be submitted directly to a subject editor or to the Editor-in-Chief if not sure about the subject area. Editorial procedures in place assure careful, fair, and prompt handling of all submitted articles. Accepted papers appear in the journal in the shortest time feasible given production time constraints.