Dynamical behavior and optimal impulse control analysis of a stochastic rumor spreading model

doi:10.1088/1674-1056/ac98fb

中国物理B ›› 2022, Vol. 31 ›› Issue (11): 110204-110204.doi: 10.1088/1674-1056/ac98fb

Dynamical behavior and optimal impulse control analysis of a stochastic rumor spreading model

Liang'an Huo(霍良安)^† and Xiaomin Chen(陈晓敏)

Business School, University of Shanghai for Science and Technology, Shanghai 200093, China

收稿日期:2021-11-15 修回日期:2022-04-13 接受日期:2022-10-11 出版日期:2022-10-17 发布日期:2022-10-19
通讯作者: Liang'an Huo E-mail:huohuolin@yeah.net
基金资助:
This work was partially supported by the Project for the National Natural Science Foundation of China (Grant Nos. 72174121 and 71774111), and the Program for Professor of Special Appointment (Eastern Scholar) at Shanghai Institutions of Higher Learning, and the Project for the Natural Science Foundation of Shanghai (Grant No. 21ZR1444100), and Project Soft Science Research of Shanghai (Grant No. 22692112600).

Dynamical behavior and optimal impulse control analysis of a stochastic rumor spreading model

Liang'an Huo(霍良安)^† and Xiaomin Chen(陈晓敏)

Business School, University of Shanghai for Science and Technology, Shanghai 200093, China

Received:2021-11-15 Revised:2022-04-13 Accepted:2022-10-11 Online:2022-10-17 Published:2022-10-19
Contact: Liang'an Huo E-mail:huohuolin@yeah.net
Supported by:
This work was partially supported by the Project for the National Natural Science Foundation of China (Grant Nos. 72174121 and 71774111), and the Program for Professor of Special Appointment (Eastern Scholar) at Shanghai Institutions of Higher Learning, and the Project for the Natural Science Foundation of Shanghai (Grant No. 21ZR1444100), and Project Soft Science Research of Shanghai (Grant No. 22692112600).

摘要/Abstract

摘要： The Internet era has brought great convenience to our life and communication. Meanwhile, it also makes a bunch of rumors propagate faster and causes even more harm to human life. Therefore, it is necessary to perform effective control mechanisms to minimize the negative social impact from rumors. Thereout, firstly, we formulate a rumor spreading model considering psychological factors and thinking time, then, we add white noise (i.e., stochastic interference) and two pulse control strategies which denote education mechanism and refutation mechanism into the model. Secondly, we obtain the global positive solutions and demonstrate the global exponential stability of the unique positive periodic rumor-free solution. Thirdly, we discuss the extinction and persistence of rumor. Moreover, we use Pontriagin's minimum principle to explore the optimal impulse control. Finally, several numerical simulations are carried out to verify the effectiveness and availability of the theoretical analysis. We conclude that the pulse control strategies have a great influence on controlling rumor spreading, and different control strategies should be adopted under different transmission scenarios.

关键词: rumor spreading, stochastic process, optimal impulse control, education mechanism, refutation mechanism

Abstract: The Internet era has brought great convenience to our life and communication. Meanwhile, it also makes a bunch of rumors propagate faster and causes even more harm to human life. Therefore, it is necessary to perform effective control mechanisms to minimize the negative social impact from rumors. Thereout, firstly, we formulate a rumor spreading model considering psychological factors and thinking time, then, we add white noise (i.e., stochastic interference) and two pulse control strategies which denote education mechanism and refutation mechanism into the model. Secondly, we obtain the global positive solutions and demonstrate the global exponential stability of the unique positive periodic rumor-free solution. Thirdly, we discuss the extinction and persistence of rumor. Moreover, we use Pontriagin's minimum principle to explore the optimal impulse control. Finally, several numerical simulations are carried out to verify the effectiveness and availability of the theoretical analysis. We conclude that the pulse control strategies have a great influence on controlling rumor spreading, and different control strategies should be adopted under different transmission scenarios.

Key words: rumor spreading, stochastic process, optimal impulse control, education mechanism, refutation mechanism

中图分类号: (Partial differential equations)

02.30.Jr

02.50.Ey (Stochastic processes) 02.50.Fz (Stochastic analysis)

Liang'an Huo(霍良安) and Xiaomin Chen(陈晓敏). Dynamical behavior and optimal impulse control analysis of a stochastic rumor spreading model[J]. 中国物理B, 2022, 31(11): 110204-110204.

Liang'an Huo(霍良安) and Xiaomin Chen(陈晓敏). Dynamical behavior and optimal impulse control analysis of a stochastic rumor spreading model[J]. Chin. Phys. B, 2022, 31(11): 110204-110204.

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Dynamical behavior and optimal impulse control analysis of a stochastic rumor spreading model

Dynamical behavior and optimal impulse control analysis of a stochastic rumor spreading model

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