IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v153y2021ip2s0960077921008183.html
   My bibliography  Save this article

Stability and Hopf bifurcation analysis of multi-lingual rumor spreading model with nonlinear inhibition mechanism

Author

Listed:
  • Wang, Jinling
  • Jiang, Haijun
  • Hu, Cheng
  • Yu, Zhiyong
  • Li, Jiarong

Abstract

The stability and hopf bifurcation of the multi-lingual rumor spreading model are mainly studied in this paper. A nonlinear inhibition mechanism is introduced to formulate an IS2R2 model with concerning the cross propagation in the multi-lingual environment. Next, the existence and stability of equilibrium points are analyzed systematically here. Meanwhile, choosing the key parameter and time delay of inhibition functions as bifurcation parameters, the characteristics of Hopf bifurcation are further displayed through certain critical values. Besides, an optimal control strategy involving inhibition functions is designed, and simulated via forward-backward sweep algorithm. Finally, the comparative analysis of various parameters in the numerical simulation is presented to justify our theoretical results.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:153:y:2021:i:p2:s0960077921008183
    DOI: 10.1016/j.chaos.2021.111464
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077921008183
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2021.111464?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. Michael McAsey & Libin Mou & Weimin Han, 2012. "Convergence of the forward-backward sweep method in optimal control," Computational Optimization and Applications, Springer, vol. 53(1), pages 207-226, September.
    2. Wang, Jinling & Jiang, Haijun & Ma, Tianlong & Hu, Cheng, 2019. "Global dynamics of the multi-lingual SIR rumor spreading model with cross-transmitted mechanism," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 148-157.
    3. Xu, Rui & Ma, Zhien, 2009. "Stability of a delayed SIRS epidemic model with a nonlinear incidence rate," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2319-2325.
    4. Xia, Ling-Ling & Jiang, Guo-Ping & Song, Bo & Song, Yu-Rong, 2015. "Rumor spreading model considering hesitating mechanism in complex social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 437(C), pages 295-303.
    5. Xiaohong Tian & Rui Xu, 2009. "Stability Analysis of a Delayed SIR Epidemic Model with Stage Structure and Nonlinear Incidence," Discrete Dynamics in Nature and Society, Hindawi, vol. 2009, pages 1-17, October.
    6. Yang, Anzhi & Huang, Xianying & Cai, Xiumei & Zhu, Xiaofei & Lu, Ling, 2019. "ILSR rumor spreading model with degree in complex network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 531(C).
    7. Zhang, Jiancheng & Sun, Jitao, 2014. "Stability analysis of an SIS epidemic model with feedback mechanism on networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 394(C), pages 24-32.
    8. Bodaghi, Amirhosein & Goliaei, Sama & Salehi, Mostafa, 2019. "The number of followings as an influential factor in rumor spreading," Applied Mathematics and Computation, Elsevier, vol. 357(C), pages 167-184.
    9. Li, Jiarong & Jiang, Haijun & Yu, Zhiyong & Hu, Cheng, 2019. "Dynamical analysis of rumor spreading model in homogeneous complex networks," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 374-385.
    10. 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).
    11. Huo, Liang’an & Wang, Li & Song, Guoxiang, 2017. "Global stability of a two-mediums rumor spreading model with media coverage," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 482(C), pages 757-771.
    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 & 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).
    2. 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).
    3. 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.
    4. 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).
    5. 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.

    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. Shuzhen Yu & Zhiyong Yu & Haijun Jiang, 2022. "Stability, Hopf Bifurcation and Optimal Control of Multilingual Rumor-Spreading Model with Isolation Mechanism," Mathematics, MDPI, vol. 10(23), pages 1-29, December.
    2. 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).
    3. Xia, Yang & Jiang, Haijun & Yu, Zhiyong, 2022. "Global dynamics of ILSR rumor spreading model with general nonlinear spreading rate in multi-lingual environment," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    4. 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).
    5. 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).
    6. Jiang, Guoyin & Li, Saipeng & Li, Minglei, 2020. "Dynamic rumor spreading of public opinion reversal on Weibo based on a two-stage SPNR model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 558(C).
    7. 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).
    8. Huo, Liang’an & Chen, Sijing, 2020. "Rumor propagation model with consideration of scientific knowledge level and social reinforcement in heterogeneous network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 559(C).
    9. Cheng, Yingying & Huo, Liang'an & Zhao, Laijun, 2022. "Stability analysis and optimal control of rumor spreading model under media coverage considering time delay and pulse vaccination," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    10. Hongying Xiao & Zhaofeng Li & Yuanyuan Zhang & Hong Lin & Yuxiao Zhao, 2023. "A Dual Rumor Spreading Model with Consideration of Fans versus Ordinary People," Mathematics, MDPI, vol. 11(13), pages 1-14, July.
    11. 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).
    12. Tong Chen & Ziqing Chen & Xuejun Jin, 2021. "A multiple information model incorporating limited attention and information environment," PLOS ONE, Public Library of Science, vol. 16(10), pages 1-22, October.
    13. 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).
    14. Li, Dandan & Qian, Wenqi & Sun, Xiaoxiao & Han, Dun & Sun, Mei, 2023. "Rumor spreading in a dual-relationship network with diverse propagation abilities," Applied Mathematics and Computation, Elsevier, vol. 458(C).
    15. Huo, Liang’an & Cheng, Yingying & Liu, Chen & Ding, Fan, 2018. "Dynamic analysis of rumor spreading model for considering active network nodes and nonlinear spreading rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 24-35.
    16. 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).
    17. Lu, Peng & Yao, Qi & Lu, Pengfei, 2019. "Two-stage predictions of evolutionary dynamics during the rumor dissemination," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 517(C), pages 349-369.
    18. Huo, Liang’an & Ding, Fan & Cheng, Yingying, 2019. "Dynamic analysis of a SIbInIu, rumor spreading model in complex social network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 924-932.
    19. Maia, Hugo P. & Ferreira, Silvio C. & Martins, Marcelo L., 2023. "Controversy-seeking fuels rumor-telling activity in polarized opinion networks," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    20. Liang’an Huo & Fan Ding & Chen Liu & Yingying Cheng, 2018. "Dynamical Analysis of Rumor Spreading Model considering Node Activity in Complex Networks," Complexity, Hindawi, vol. 2018, pages 1-10, November.

    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:153:y:2021:i:p2:s0960077921008183. 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.