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Dynamics of a Predator–Prey Model with the Additive Predation in Prey

Author

Listed:
  • Dingyong Bai

    (School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China
    Guangzhou Center for Applied Mathematics, Guangzhou University, Guangzhou 510006, China
    These authors contributed equally to this work.)

  • Xiaoxuan Zhang

    (School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China
    Guangzhou Center for Applied Mathematics, Guangzhou University, Guangzhou 510006, China
    These authors contributed equally to this work.)

Abstract

In this paper, we consider a predator–prey model, in which the prey’s growth is affected by the additive predation of its potential predators. Due to the additive predation term in prey, the model may exhibit the cases of the strong Allee effect, weak Allee effect and no Allee effect. In each case, the dynamics of global features of the model are investigated. Compared to the well-known Lotka–Volterra type model, the model proposed in this paper exhibits much richer and more complex dynamic behaviors, such as the Allee effect, the sensitivity to the initial conditions caused by the strong Allee effect, the oscillatory behavior and the Hopf and heteroclinic bifurcations. Furthermore, the stability and Hopf bifurcation of the model with the density dependent feedback time delay in prey are investigated. By the normal form method and center manifold theory, the explicit formulas are presented to determine the direction of Hopf bifurcation and the stability and period of Hopf-bifurcating periodic solutions. Theoretical analysis and numerical simulation indicate that the delay may destabilize the model, and cause the Hopf bifurcation not only at the interior equilibrium but also at a boundary equilibrium.

Suggested Citation

  • Dingyong Bai & Xiaoxuan Zhang, 2022. "Dynamics of a Predator–Prey Model with the Additive Predation in Prey," Mathematics, MDPI, vol. 10(4), pages 1-30, February.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:4:p:655-:d:753775
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    References listed on IDEAS

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    1. Panday, Pijush & Samanta, Sudip & Pal, Nikhil & Chattopadhyay, Joydev, 2020. "Delay induced multiple stability switch and chaos in a predator–prey model with fear effect," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 172(C), pages 134-158.
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