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

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  • 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, John Wiley & Sons, vol. 2019(1).
    • Handle: RePEc:wly:jnlamp:v:2019:y:2019:i:1:n:7296461
    DOI: 10.1155/2019/7296461
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    References listed on IDEAS

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    1. Li, Yilong & Xiao, Dongmei, 2007. "Bifurcations of a predator–prey system of Holling and Leslie types," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 606-620.
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    Cited by:

    1. Rebelo, Paulo & Rosa, Silvério, 2025. "An optimal control problem for a predator–prey model with strong and weak preys," Chaos, Solitons & Fractals, Elsevier, vol. 191(C).
    2. Abayneh Fentie Bezabih & Geremew Kenassa Edessa & Koya Purnachandra Rao, 2021. "Ecoepidemiological Model and Analysis of Prey‐Predator System," Journal of Applied Mathematics, John Wiley & Sons, vol. 2021(1).

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