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Hopf Bifurcation Analysis of a Class of Saperda populnea Infectious Disease Model with Delay

Author

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  • Fuyu Cai

    (Department of Mathematics, Northeast Forestry University, Harbin 150040, China)

  • Yuting Ding

    (Department of Mathematics, Northeast Forestry University, Harbin 150040, China)

Abstract

Under the background of double carbon, it is important to study forest pests and diseases to improve forest carbon sink. In this paper, we establish a delayed model associated with the larvae and adults of Saperda populnea , susceptible poplars, and infected poplars. First, we analyze the existence and stability of the equilibrium of the model. Second, we study the existence of Hopf bifurcation near the equilibrium and obtain the normal form of Hopf bifurcation by the multiple time scales method. Then, we analyze the direction and stability of Hopf bifurcating periodic solutions. Third, we analyze and conjecture some parameter values based on official data, and carry out numerical simulations to verify our results. Finally, we give some suggestions on the prevention and control of Saperda populnea .

Suggested Citation

  • Fuyu Cai & Yuting Ding, 2023. "Hopf Bifurcation Analysis of a Class of Saperda populnea Infectious Disease Model with Delay," Mathematics, MDPI, vol. 11(20), pages 1-14, October.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:20:p:4225-:d:1256438
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    References listed on IDEAS

    as
    1. Xiao Wang & Yufu Ning, 2019. "A New Stability Analysis of Uncertain Delay Differential Equations," Mathematical Problems in Engineering, Hindawi, vol. 2019, pages 1-8, January.
    2. Wang, Qunwei & Chiu, Yung-Ho & Chiu, Ching-Ren, 2015. "Driving factors behind carbon dioxide emissions in China: A modified production-theoretical decomposition analysis," Energy Economics, Elsevier, vol. 51(C), pages 252-260.
    3. Xu, Shi-Chun & He, Zheng-Xia & Long, Ru-Yin, 2014. "Factors that influence carbon emissions due to energy consumption in China: Decomposition analysis using LMDI," Applied Energy, Elsevier, vol. 127(C), pages 182-193.
    4. Abraha, Teklebirhan & Al Basir, Fahad & Obsu, Legesse Lemecha & Torres, Delfim F.M., 2021. "Pest control using farming awareness: Impact of time delays and optimal use of biopesticides," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    Full references (including those not matched with items on IDEAS)

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