IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v166y2023ics0960077922011493.html
   My bibliography  Save this article

Pattern study and parameter identification of a reaction-diffusion rumor propagation system with time delay

Author

Listed:
  • Zhu, Linhe
  • Tang, Yuxuan
  • Shen, Shuling

Abstract

In this paper, a reaction-diffusion dynamic model with time delay is established under the background of network rumors, and the behavior of susceptible users and infected users in spreading rumors on the network is analyzed to help us study the mechanism of rumor propagation. Firstly, the Turing instability condition of delay approximate system is studied. Secondly, based on the amplitude equation method, the theoretical conditions of different patterns near Turing bifurcation point are given, and different types of Turing patterns are divided. Then, the accuracy of the theory is verified by numerical simulation under different parameters, and the effectiveness of the model is verified by Monte Carlo simulation. In addition, the effects of different networks and time-delay conditions on pattern formation are studied. Finally, in order to help the model apply to the actual situation, the parameter identification and optimization control of the system are carried out.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:166:y:2023:i:c:s0960077922011493
    DOI: 10.1016/j.chaos.2022.112970
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077922011493
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2022.112970?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Huo, Liang’an & Song, Naixiang, 2016. "Dynamical interplay between the dissemination of scientific knowledge and rumor spreading in emergency," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 73-84.
    2. Zheng, Qianqian & Shen, Jianwei & Xu, Yong & Pandey, Vikas & Guan, Linan, 2022. "Pattern mechanism in stochastic SIR networks with ER connectivity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 603(C).
    3. Chen, Shanshan & Jiang, Haijun & Li, Liang & Li, Jiarong, 2020. "Dynamical behaviors and optimal control of rumor propagation model with saturation incidence on heterogeneous networks," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    4. 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).
    5. Lakshmi Narayan Guin & Reeta Murmu & Hunki Baek & Kyoung-Hwan Kim, 2020. "Dynamical Analysis of a Beddington–DeAngelis Interacting Species System with Prey Harvesting," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-22, October.
    6. Guin, Lakshmi Narayan, 2015. "Spatial patterns through Turing instability in a reaction–diffusion predator–prey model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 109(C), pages 174-185.
    7. Li, Qiang & Liu, Zhijun & Yuan, Sanling, 2019. "Cross-diffusion induced Turing instability for a competition model with saturation effect," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 64-77.
    8. Guo, Zun-Guang & Sun, Gui-Quan & Wang, Zhen & Jin, Zhen & Li, Li & Li, Can, 2020. "Spatial dynamics of an epidemic model with nonlocal infection," Applied Mathematics and Computation, Elsevier, vol. 377(C).
    9. 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).
    10. Chen, Mengxin & Wu, Ranchao & Chen, Liping, 2020. "Spatiotemporal patterns induced by Turing and Turing-Hopf bifurcations in a predator-prey system," Applied Mathematics and Computation, Elsevier, vol. 380(C).
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. Cao, Yuan & Su, Shuai, 2023. "Fractional gradient descent algorithms for systems with outliers: A matrix fractional derivative or a scalar fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    4. Tang, Jia, 2023. "Fractional gradient descent algorithm for switching models using self-organizing maps: One set data or all the collected data," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Xuefeng Yue & Liangan Huo, 2022. "Analysis of the Stability and Optimal Control Strategy for an ISCR Rumor Propagation Model with Saturated Incidence and Time Delay on a Scale-Free Network," Mathematics, MDPI, vol. 10(20), pages 1-20, October.
    2. Dong, Yafang & Huo, Liang'an & Zhao, Laijun, 2022. "An improved two-layer model for rumor propagation considering time delay and event-triggered impulsive control strategy," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    3. Souna, Fethi & Belabbas, Mustapha & Menacer, Youssaf, 2023. "Complex pattern formations induced by the presence of cross-diffusion in a generalized predator–prey model incorporating the Holling type functional response and generalization of habitat complexity e," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 597-618.
    4. Chen, Mengxin & Wu, Ranchao, 2023. "Steady states and spatiotemporal evolution of a diffusive predator–prey model," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    5. 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.
    6. Hu, Junlang & Zhu, Linhe, 2021. "Turing pattern analysis of a reaction-diffusion rumor propagation system with time delay in both network and non-network environments," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    7. Jing Chen & Nana Wei & Chen Xin & Mingxin Liu & Zeren Yu & Miaomiao Liu, 2022. "Anti-Rumor Dissemination Model Based on Heat Influence and Evolution Game," Mathematics, MDPI, vol. 10(21), pages 1-15, November.
    8. Wang, Chuanbiao & Liu, Ruiying & Wang, Yan, 2023. "The spread dynamics model of the interaction between rumors and derivative rumors in emergencies under the control strategy," Chaos, Solitons & Fractals, Elsevier, vol. 175(P2).
    9. Yin, Fulian & Jiang, Xinyi & Qian, Xiqing & Xia, Xinyu & Pan, Yanyan & Wu, Jianhong, 2022. "Modeling and quantifying the influence of rumor and counter-rumor on information propagation dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    10. Ma, Yuanyuan & Dong, Nan & Liu, Na & Xie, Leilei, 2022. "Spatiotemporal and bifurcation characteristics of a nonlinear prey-predator model," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    11. Yu, Shuzhen & Yu, Zhiyong & Jiang, Haijun, 2024. "A rumor propagation model in multilingual environment with time and state dependent impulsive control," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    12. Xu, Li & Liu, Jiayi & Zhang, Guang, 2018. "Pattern formation and parameter inversion for a discrete Lotka–Volterra cooperative system," Chaos, Solitons & Fractals, Elsevier, vol. 110(C), pages 226-231.
    13. Chen, Zheng & Wu, Yong-Ping & Feng, Guo-Lin & Qian, Zhong-Hua & Sun, Gui-Quan, 2021. "Effects of global warming on pattern dynamics of vegetation: Wuwei in China as a case," Applied Mathematics and Computation, Elsevier, vol. 390(C).
    14. Liu, Chen & Wang, Fang-Guang & Xue, Qiang & Li, Li & Wang, Zhen, 2022. "Pattern formation of a spatial vegetation system with root hydrotropism," Applied Mathematics and Computation, Elsevier, vol. 420(C).
    15. Zhu, He & Ma, Jing, 2018. "Knowledge diffusion in complex networks by considering time-varying information channels," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 494(C), pages 225-235.
    16. He, Le & Su, Haijun, 2024. "Spatiotemporal patterns of reaction–diffusion systems with advection mechanisms on large-scale regular networks," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    17. M., Pitchaimani & M., Brasanna Devi, 2020. "Random effects in HIV infection model at Eclipse stage," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 554(C).
    18. Wen, Zijuan & Fu, Shengmao, 2016. "Turing instability for a competitor-competitor-mutualist model with nonlinear cross-diffusion effects," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 379-385.
    19. Wang, Fatao & Yang, Ruizhi, 2023. "Spatial pattern formation driven by the cross-diffusion in a predator–prey model with Holling type functional response," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    20. Chen, Xiaolong & Gong, Kai & Wang, Ruijie & Cai, Shimin & Wang, Wei, 2020. "Effects of heterogeneous self-protection awareness on resource-epidemic coevolution dynamics," Applied Mathematics and Computation, Elsevier, vol. 385(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:166:y:2023:i:c:s0960077922011493. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.