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Dynamics of a reaction-diffusion rumor propagation model with non-smooth control

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  • Ke, Yue
  • Zhu, Linhe
  • Wu, Peng
  • Shi, Lei

Abstract

To reflect the government and media refutation to rumor propagation, we have established a reaction-diffusion rumor propagation model by considering a non-smooth control function. Firstly, we obtain the rumor propagation threshold according to the next generation matrix theory, prove the existence and uniqueness of solution and discuss the existence of the equilibrium points. Secondly, we discuss the stability of the equilibrium points with the impact of the spatial diffusion. Thirdly, the conditions for spatially homogeneous and discontinuous Hopf bifurcation are presented. Finally, several numerical simulations are given to show the possible impact, and the factors affecting rumor propagation are theoretically analyzed, which proves the validity of the theoretical analysis.

Suggested Citation

  • Ke, Yue & Zhu, Linhe & Wu, Peng & Shi, Lei, 2022. "Dynamics of a reaction-diffusion rumor propagation model with non-smooth control," Applied Mathematics and Computation, Elsevier, vol. 435(C).
    • Handle: RePEc:eee:apmaco:v:435:y:2022:i:c:s0096300322005525
    DOI: 10.1016/j.amc.2022.127478
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    References listed on IDEAS

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    Cited by:

    1. Xiaojing Zhong & Yawen Zheng & Junxian Xie & Ying Xie & Yuqing Peng, 2024. "Multi-Agent Collaborative Rumor-Debunking Strategies on Virtual-Real Network Layer," Mathematics, MDPI, vol. 12(3), pages 1-22, January.
    2. Zhu, Linhe & Zheng, Wenxin & Shen, Shuling, 2023. "Dynamical analysis of a SI epidemic-like propagation model with non-smooth control," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    3. Tian, Yang & Tian, Hui & Cui, Qimei & Zhu, Xuzhen, 2024. "Phase transition phenomena in social propagation with dynamic fashion tendency and individual contact," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    4. Zhu, Linhe & Chen, Siyi & Shen, Shuling, 2024. "Pattern dynamics analysis of a reaction–diffusion network propagation model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 220(C), pages 425-444.
    5. Dong, Yafang & Huo, Liang’an, 2024. "A multi-scale mathematical model of rumor propagation considering both intra- and inter-individual dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 185(C).
    6. Yanchao Liu & Pengzhou Zhang & Lei Shi & Junpeng Gong, 2023. "A Survey of Information Dissemination Model, Datasets, and Insight," Mathematics, MDPI, vol. 11(17), pages 1-30, August.
    7. Pan, Yuxuan & Zhu, Linhe, 2024. "Parameter identification method of information propagation models based on different network structures," Chaos, Solitons & Fractals, Elsevier, vol. 185(C).

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