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Stability and Bifurcation Analysis on a Predator–Prey System with the Weak Allee Effect

Author

Listed:
  • Jianming Zhang

    (Department of Mathematics, School of Science, Zhejiang Sci-Tech University, Hangzhou 310018, China)

  • Lijun Zhang

    (College of Mathematics and Systems Science, Shandong University of Science and Technology Qingdao 266590, China)

  • Yuzhen Bai

    (School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China)

Abstract

In this paper, the dynamics of a predator-prey system with the weak Allee effect is considered. The sufficient conditions for the existence of Hopf bifurcation and stability switches induced by delay are investigated. By using the theory of normal form and center manifold, an explicit expression, which can be applied to determine the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions, are obtained. Numerical simulations are performed to illustrate the theoretical analysis results.

Suggested Citation

  • Jianming Zhang & Lijun Zhang & Yuzhen Bai, 2019. "Stability and Bifurcation Analysis on a Predator–Prey System with the Weak Allee Effect," Mathematics, MDPI, vol. 7(5), pages 1-15, May.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:5:p:432-:d:231697
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    References listed on IDEAS

    as
    1. Jianming Zhang & Lijun Zhang & Chaudry Masood Khalique, 2014. "Stability and Hopf Bifurcation Analysis on a Bazykin Model with Delay," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-7, March.
    2. Manna, Debasis & Maiti, Alakes & Samanta, G.P., 2017. "A Michaelis–Menten type food chain model with strong Allee effect on the prey," Applied Mathematics and Computation, Elsevier, vol. 311(C), pages 390-409.
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    Cited by:

    1. Xiaorong Ma & Qamar Din & Muhammad Rafaqat & Nasir Javaid & Yongliang Feng, 2020. "A Density-Dependent Host-Parasitoid Model with Stability, Bifurcation and Chaos Control," Mathematics, MDPI, vol. 8(4), pages 1-26, April.
    2. Jing Li & Yuying Chen & Shaotao Zhu, 2022. "Periodic Solutions and Stability Analysis for Two-Coupled-Oscillator Structure in Optics of Chiral Molecules," Mathematics, MDPI, vol. 10(11), pages 1-24, June.

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