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Dynamical analysis of rumor spreading model in homogeneous complex networks

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  • Li, Jiarong
  • Jiang, Haijun
  • Yu, Zhiyong
  • Hu, Cheng

Abstract

In this paper, an I2S2R rumor spreading model in complex networks is established and analyzed. Firstly, the threshold value is acquired to identify the existence and stability of rumor-free equilibria state and rumor equilibria state by using the next generation matrix method. Secondly, based on Routh–Hurwitz judgment, Lyapunov stability theory and LaSalle’s invariance principle, the local and global stability of rumor-free/rumor equilibrium points are discussed. Thirdly, the sensitivity analysis about the threshold value is given to analyze the impact of model parameters on rumor propagation. Finally, some numerical simulations are presented to illustrate the validity and feasibility of corresponding results.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:359:y:2019:i:c:p:374-385
    DOI: 10.1016/j.amc.2019.04.076
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    as
    1. Wang, Jing & Hu, Xiaohui & Wei, Yunliang & Wang, Zhen, 2019. "Sampled-data synchronization of semi-Markov jump complex dynamical networks subject to generalized dissipativity property," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 853-864.
    2. Li, Dandan & Ma, Jing, 2017. "How the government’s punishment and individual’s sensitivity affect the rumor spreading in online social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 469(C), pages 284-292.
    3. Zhang, Yuhuai & Zhu, Jianjun, 2018. "Stability analysis of I2S2R rumor spreading model in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 862-881.
    4. Huang, Zhengguo & Xia, Jianwei & Wang, Jing & Wei, Yunliang & Wang, Zhen & Wang, Jian, 2019. "Mixed H∞/l2−l∞ state estimation for switched genetic regulatory networks subject to packet dropouts: A persistent dwell-time switching mechanism," Applied Mathematics and Computation, Elsevier, vol. 355(C), pages 198-212.
    5. Wang, Jiajia & Zhao, Laijun & Huang, Rongbing, 2014. "2SI2R rumor spreading model in homogeneous networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 413(C), pages 153-161.
    6. 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.
    7. 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.
    8. Liu, Qiming & Li, Tao & Sun, Meici, 2017. "The analysis of an SEIR rumor propagation model on heterogeneous network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 469(C), pages 372-380.
    9. Afassinou, Komi, 2014. "Analysis of the impact of education rate on the rumor spreading mechanism," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 414(C), pages 43-52.
    10. Zan, Yongli, 2018. "DSIR double-rumors spreading model in complex networks," Chaos, Solitons & Fractals, Elsevier, vol. 110(C), pages 191-202.
    11. Huo, Liang'an & Wang, Li & Song, Naixiang & Ma, Chenyang & He, Bing, 2017. "Rumor spreading model considering the activity of spreaders in the homogeneous network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 855-865.
    12. Zhao, Laijun & Wang, Xiaoli & Qiu, Xiaoyan & Wang, Jiajia, 2013. "A model for the spread of rumors in Barrat–Barthelemy–Vespignani (BBV) networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(21), pages 5542-5551.
    13. 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.
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