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Pattern dynamics analysis of a reaction–diffusion network propagation model

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  • Zhu, Linhe
  • Chen, Siyi
  • Shen, Shuling

Abstract

In this paper, considering the spatial propagation behavior of Internet rumor, we propose a new reaction–diffusion rumor propagation model with time delay in social networks. Based on this, we discuss the stability conditions at the equilibrium point and analyze the Turing instability for the approximation propagation system. Simultaneously, the amplitude equations for the approximation system are derived by multiscale analysis. We use numerical simulation to compare the effect of parameter size, period, and time delay on the patterns. Moreover, we compare the different reactivity of the system in the WS networks and the BA networks. Finally, we plot the corresponding amplitude equations patterns by controlling the parameters and verify the correctness of the theoretical results.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:220:y:2024:i:c:p:425-444
    DOI: 10.1016/j.matcom.2024.01.025
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    References listed on IDEAS

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    1. Dong, Suyalatu & Fan, Feng-Hua & Huang, Yong-Chang, 2018. "Studies on the population dynamics of a rumor-spreading model in online social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 492(C), pages 10-20.
    2. Zhu, Liang & Wang, Youguo, 2018. "Rumor diffusion model with spatio-temporal diffusion and uncertainty of behavior decision in complex social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 502(C), pages 29-39.
    3. Lazebnik, Teddy, 2023. "Computational applications of extended SIR models: A review focused on airborne pandemics," Ecological Modelling, Elsevier, vol. 483(C).
    4. Tyagi, Swati & Martha, Subash C. & Abbas, Syed & Debbouche, Amar, 2021. "Mathematical modeling and analysis for controlling the spread of infectious diseases," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    5. Xu, Hao & Li, Tao & Liu, Xiongding & Liu, Wenjin & Dong, Jing, 2019. "Spreading dynamics of an online social rumor model with psychological factors on scale-free networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 234-246.
    6. Zhu, Linhe & Tang, Yuxuan & Shen, Shuling, 2023. "Pattern study and parameter identification of a reaction-diffusion rumor propagation system with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    7. Zhang, Ziyu & Mei, Xuehui & Jiang, Haijun & Luo, Xupeng & Xia, Yang, 2023. "Dynamical analysis of Hyper-SIR rumor spreading model," Applied Mathematics and Computation, Elsevier, vol. 446(C).
    8. 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).
    9. Nwaibeh, E.A. & Chikwendu, C.R., 2023. "A deterministic model of the spread of scam rumor and its numerical simulations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 207(C), pages 111-129.
    10. Wang, Jinling & Jiang, Haijun & Hu, Cheng & Yu, Zhiyong & Li, Jiarong, 2021. "Stability and Hopf bifurcation analysis of multi-lingual rumor spreading model with nonlinear inhibition mechanism," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
    11. Yu, Shuzhen & Yu, Zhiyong & Jiang, Haijun & Li, Jiarong, 2021. "Dynamical study and event-triggered impulsive control of rumor propagation model on heterogeneous social network incorporating delay," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    12. Zhang, Xi & Cheng, Yihang & Chen, Aoshuang & Lytras, Miltiadis & de Pablos, Patricia Ordóñez & Zhang, Renyu, 2022. "How rumors diffuse in the infodemic: Evidence from the healthy online social change in China," Technological Forecasting and Social Change, Elsevier, vol. 185(C).
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