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Dynamical Analysis of a Delayed Diffusive Predator–Prey Model with Additional Food Provided and Anti-Predator Behavior

Author

Listed:
  • Ruizhi Yang

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

  • Xiao Zhao

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

  • Yong An

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

Abstract

We studied a delayed predator–prey model with diffusion and anti-predator behavior. Assume that additional food is provided for predator population. Then the stability of the positive equilibrium is considered. The existence of Hopf bifurcation is also discussed based on the Hopf bifurcation theory. The property of Hopf bifurcation is derived through the theory of center manifold and normal form method. Finally, we analyze the effect of time delay on the model through numerical simulations.

Suggested Citation

  • Ruizhi Yang & Xiao Zhao & Yong An, 2022. "Dynamical Analysis of a Delayed Diffusive Predator–Prey Model with Additional Food Provided and Anti-Predator Behavior," Mathematics, MDPI, vol. 10(3), pages 1-18, January.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:3:p:469-:d:739419
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    Citations

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    Cited by:

    1. He, Haoming & Xiao, Min & He, Jiajin & Zheng, Weixing, 2024. "Regulating spatiotemporal dynamics for a delay Gierer–Meinhardt model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 637(C).
    2. Abbasi, Muhammad Aqib & Samreen, Maria, 2024. "Analyzing multi-parameter bifurcation on a prey–predator model with the Allee effect and fear effect," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    3. Wenqi Zhang & Dan Jin & Ruizhi Yang, 2023. "Hopf Bifurcation in a Predator–Prey Model with Memory Effect in Predator and Anti-Predator Behaviour in Prey," Mathematics, MDPI, vol. 11(3), pages 1-12, January.
    4. Jiao, Xubin & Li, Xiaodi & Yang, Youping, 2022. "Dynamics and bifurcations of a Filippov Leslie-Gower predator-prey model with group defense and time delay," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).

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