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Global stability of a rumor spreading model with discontinuous control strategies

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  • Zhu, Honglan
  • Zhang, Xuebing
  • An, Qi

Abstract

With the rapid development of online media in recent years, rumors have also proliferated and spread. If they are not effectively managed, they will cause great harm to society. So, how to stop the spread of rumors has become a hot topic that needs to be studied. In this study, we consider a rumor spreading model with discontinuous control strategies. According to differential inclusion theory, we investigate the existence and boundedness of the solution of the model. By the theory of topological degree, we derive some conditions for the existence of the equilibria of the model, as well as studying the global asymptotic stability of the rumor-free equilibrium and the positive equilibrium. Finally, we study global convergence in finite time. These findings can aid in the development of rumor-control policies. The study may have important implications for effectively predicting and preventing rumor spread.

Suggested Citation

  • Zhu, Honglan & Zhang, Xuebing & An, Qi, 2022. "Global stability of a rumor spreading model with discontinuous control strategies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 606(C).
    • Handle: RePEc:eee:phsmap:v:606:y:2022:i:c:s0378437122007154
    DOI: 10.1016/j.physa.2022.128157
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    References listed on IDEAS

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    1. Zhu, He & Ma, Jing, 2019. "Analysis of SHIR rumor propagation in random heterogeneous networks with dynamic friendships," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 513(C), pages 257-271.
    2. Zhao, Laijun & Cui, Hongxin & Qiu, Xiaoyan & Wang, Xiaoli & Wang, Jiajia, 2013. "SIR rumor spreading model in the new media age," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(4), pages 995-1003.
    3. Huo, Liang’an & Wang, Li & Zhao, Xiaomin, 2019. "Stability analysis and optimal control of a rumor spreading model with media report," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 517(C), pages 551-562.
    4. Zhu, Linhe & Liu, Mengxue & Li, Yimin, 2019. "The dynamics analysis of a rumor propagation model in online social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 520(C), pages 118-137.
    5. Chen, Guanghua, 2019. "ILSCR rumor spreading model to discuss the control of rumor spreading in emergency," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 522(C), pages 88-97.
    6. Zhu, Linhe & Liu, Wenshan & Zhang, Zhengdi, 2020. "Delay differential equations modeling of rumor propagation in both homogeneous and heterogeneous networks with a forced silence function," Applied Mathematics and Computation, Elsevier, vol. 370(C).
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    1. Li, Shunjie & Zhang, Xuebing & An, Qi, 2024. "A rumor spreading multi-delay model with delay-dependent parameter," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 223(C), pages 34-49.

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