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Bifurcation Analysis for an OSN Model with Two Delays

Author

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  • Liancheng Wang

    (Department of Mathematics, Kennesaw State University, Marietta, GA 30060, USA)

  • Min Wang

    (Department of Mathematics, Kennesaw State University, Marietta, GA 30060, USA)

Abstract

In this research, we introduce and analyze a mathematical model for online social networks, incorporating two distinct delays. These delays represent the time it takes for active users within the network to begin disengaging, either with or without contacting non-users of online social platforms. We focus particularly on the user prevailing equilibrium (UPE), denoted as P * , and explore the role of delays as parameters in triggering Hopf bifurcations. In doing so, we find the conditions under which Hopf bifurcations occur, then establish stable regions based on the two delays. Furthermore, we delineate the boundaries of stability regions wherein bifurcations transpire as the delays cross these thresholds. We present numerical simulations to illustrate and validate our theoretical findings. Through this interdisciplinary approach, we aim to deepen our understanding of the dynamics inherent in online social networks.

Suggested Citation

  • Liancheng Wang & Min Wang, 2024. "Bifurcation Analysis for an OSN Model with Two Delays," Mathematics, MDPI, vol. 12(9), pages 1-17, April.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:9:p:1321-:d:1383618
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    References listed on IDEAS

    as
    1. Graef, John R. & Kong, Lingju & Ledoan, Andrew & Wang, Min, 2020. "Stability analysis of a fractional online social network model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 178(C), pages 625-645.
    2. Bettencourt, Luís M.A. & Cintrón-Arias, Ariel & Kaiser, David I. & Castillo-Chávez, Carlos, 2006. "The power of a good idea: Quantitative modeling of the spread of ideas from epidemiological models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 364(C), pages 513-536.
    3. Zhang, Jiajia & Qiao, Yuanhua, 2023. "Bifurcation analysis of an SIR model considering hospital resources and vaccination," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 208(C), pages 157-185.
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