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Dynamic Study of a Predator-Prey Model with Weak Allee Effect and Delay

Author

Listed:
  • Yong Ye
  • Hua Liu
  • Yu-mei Wei
  • Ming Ma
  • Kai Zhang

Abstract

In this paper, a prey-predator model and weak Allee effect in prey growth and its dynamical behaviors are studied in detail. The existence, boundedness, and stability of the equilibria of the model are qualitatively discussed. Bifurcation analysis is also taken into account. After incorporating the searching delay and digestion delay, we establish a delayed predator-prey system with Allee effect. The results show that there exist stability switches and Hopf bifurcation occurs while the delay crosses a set of critical values. Finally, we present some numerical simulations to illustrate our theoretical analysis.

Suggested Citation

  • Yong Ye & Hua Liu & Yu-mei Wei & Ming Ma & Kai Zhang, 2019. "Dynamic Study of a Predator-Prey Model with Weak Allee Effect and Delay," Advances in Mathematical Physics, Hindawi, vol. 2019, pages 1-15, August.
    • Handle: RePEc:hin:jnlamp:7296461
    DOI: 10.1155/2019/7296461
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    Cited by:

    1. Lei Shi & Jiaying Zhou & Yong Ye, 2023. "Pattern Formation in a Predator–Prey Model with Allee Effect and Hyperbolic Mortality on Multiplex Networks," Mathematics, MDPI, vol. 11(15), pages 1-15, July.
    2. Das, Amartya & Samanta, G.P., 2021. "Influence of environmental noises on a prey–predator species with predator-dependent carrying capacity in alpine meadow ecosystem," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 1294-1316.
    3. Yurong Dong & Hua Liu & Yumei Wei & Qibin Zhang & Gang Ma, 2024. "Stability and Hopf Bifurcation Analysis of a Predator–Prey Model with Weak Allee Effect Delay and Competition Delay," Mathematics, MDPI, vol. 12(18), pages 1-24, September.
    4. Toni Bakhtiar & Ihza Rizkia Fitri & Farida Hanum & Ali Kusnanto, 2022. "Mathematical Model of Pest Control Using Different Release Rates of Sterile Insects and Natural Enemies," Mathematics, MDPI, vol. 10(6), pages 1-18, March.
    5. Mandal, Dibyendu Sekhar & Chekroun, Abdennasser & Samanta, Sudip & Chattopadhyay, Joydev, 2021. "A mathematical study of a crop-pest–natural enemy model with Z-type control," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 468-488.

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