具有时滞和媒介的群体行为动态建模与最优控制

IF 3.2 Q2 AUTOMATION & CONTROL SYSTEMS

Systems Science & Control Engineering Pub Date : 2022-09-26 DOI:10.1080/21642583.2022.2123059

Zhenyong Li, Ting Li, Wei-jun Xu, Yan Shao

{"title":"具有时滞和媒介的群体行为动态建模与最优控制","authors":"Zhenyong Li, Ting Li, Wei-jun Xu, Yan Shao","doi":"10.1080/21642583.2022.2123059","DOIUrl":null,"url":null,"abstract":"ABSTRACT A dynamic model of herd behaviour with delay time and media is established and analysed to discover the latent mechanism that represents how capital flows in the stock market. We prove that solutions of the model are uniformly bounded, and the contagion threshold is obtained. The stability of positive equilibrium points of the model with zero and nonzero delay is discussed. An optimal control problem with media is formulated, and Pontryagin's maximum principle is applied to find an optimal strategy to control herding. Several numerical simulations show the effect of media and delay on herd behaviour. Finally, the practical meaning of the presented model is briefly discussed.","PeriodicalId":46282,"journal":{"name":"Systems Science & Control Engineering","volume":"10 1","pages":"789 - 801"},"PeriodicalIF":3.2000,"publicationDate":"2022-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Dynamic modelling and optimal control of herd behaviour with time delay and media\",\"authors\":\"Zhenyong Li, Ting Li, Wei-jun Xu, Yan Shao\",\"doi\":\"10.1080/21642583.2022.2123059\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"ABSTRACT A dynamic model of herd behaviour with delay time and media is established and analysed to discover the latent mechanism that represents how capital flows in the stock market. We prove that solutions of the model are uniformly bounded, and the contagion threshold is obtained. The stability of positive equilibrium points of the model with zero and nonzero delay is discussed. An optimal control problem with media is formulated, and Pontryagin's maximum principle is applied to find an optimal strategy to control herding. Several numerical simulations show the effect of media and delay on herd behaviour. Finally, the practical meaning of the presented model is briefly discussed.\",\"PeriodicalId\":46282,\"journal\":{\"name\":\"Systems Science & Control Engineering\",\"volume\":\"10 1\",\"pages\":\"789 - 801\"},\"PeriodicalIF\":3.2000,\"publicationDate\":\"2022-09-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Systems Science & Control Engineering\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1080/21642583.2022.2123059\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"AUTOMATION & CONTROL SYSTEMS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Systems Science & Control Engineering","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/21642583.2022.2123059","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}

引用次数: 1

摘要

摘要建立了具有时滞和媒介的羊群行为动态模型，并对其进行了分析，揭示了股票市场中资本流动的潜在机制。我们证明了模型的解是一致有界的，并得到了传染阈值。讨论了时滞为零和非零的模型正平衡点的稳定性。建立了一个有介质的最优控制问题，并应用庞特里亚金极大值原理寻找控制羊群的最优策略。几个数值模拟显示了媒介和延迟对群体行为的影响。最后，简要讨论了该模型的实际意义。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Dynamic modelling and optimal control of herd behaviour with time delay and media

ABSTRACT A dynamic model of herd behaviour with delay time and media is established and analysed to discover the latent mechanism that represents how capital flows in the stock market. We prove that solutions of the model are uniformly bounded, and the contagion threshold is obtained. The stability of positive equilibrium points of the model with zero and nonzero delay is discussed. An optimal control problem with media is formulated, and Pontryagin's maximum principle is applied to find an optimal strategy to control herding. Several numerical simulations show the effect of media and delay on herd behaviour. Finally, the practical meaning of the presented model is briefly discussed.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Systems Science & Control Engineering AUTOMATION & CONTROL SYSTEMS-

CiteScore

9.50

自引率

2.40%

发文量

审稿时长

29 weeks

期刊介绍： Systems Science & Control Engineering is a world-leading fully open access journal covering all areas of theoretical and applied systems science and control engineering. The journal encourages the submission of original articles, reviews and short communications in areas including, but not limited to: · artificial intelligence · complex systems · complex networks · control theory · control applications · cybernetics · dynamical systems theory · operations research · systems biology · systems dynamics · systems ecology · systems engineering · systems psychology · systems theory