Dynamics of a predator-prey model with strong Allee effect and nonconstant mortality rate

Juan Ye; Yi Wang; Zhan Jin; Chuanjun Dai; Min Zhao; Juan Ye; Yi Wang; Zhan Jin; Chuanjun Dai; Min Zhao

doi:10.3934/mbe.2022157

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 4: 3402-3426. doi: 10.3934/mbe.2022157

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Dynamics of a predator-prey model with strong Allee effect and nonconstant mortality rate

1.
Zhejiang Provincial Key Laboratory for Water Environment and Marine Biological Resources Protection, Wenzhou University, Wenzhou, Zhejiang 325035, China
2.
School of Mathematics and Physics, Wenzhou University, Wenzhou, Zhejiang 325035, China
3.
School of Life and Environmental Science, Wenzhou University, Wenzhou, Zhejiang 325035, China

Academic Editor: Hermann J. Eberl

Received: 23 November 2021 Revised: 02 January 2022 Accepted: 11 January 2022 Published: 25 January 2022

In this paper, dynamics analysis for a predator-prey model with strong Allee effect and nonconstant mortality rate are taken into account. We systematically studied the existence and stability of the equilibria, and detailedly analyzed various bifurcations, including transcritical, saddle-node, Hopf and Bogdanov-Takens bifurcation. In addition, the theoretical results are verified by numerical simulations. The results indicate that when the mortality is large, the nonconstant death rate can be approximated to a constant value. However, it cannot be considered constant under small mortality rate conditions. Unlike the extinction of species for the constant mortality, the nonconstant mortality may result in the coexistence of prey and predator for the predator-prey model with Allee effect.
- Allee effect,
- nonconstant mortality,
- stability,
- bifurcation
Citation: Juan Ye, Yi Wang, Zhan Jin, Chuanjun Dai, Min Zhao. Dynamics of a predator-prey model with strong Allee effect and nonconstant mortality rate[J]. Mathematical Biosciences and Engineering, 2022, 19(4): 3402-3426. doi: 10.3934/mbe.2022157

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Abstract

In this paper, dynamics analysis for a predator-prey model with strong Allee effect and nonconstant mortality rate are taken into account. We systematically studied the existence and stability of the equilibria, and detailedly analyzed various bifurcations, including transcritical, saddle-node, Hopf and Bogdanov-Takens bifurcation. In addition, the theoretical results are verified by numerical simulations. The results indicate that when the mortality is large, the nonconstant death rate can be approximated to a constant value. However, it cannot be considered constant under small mortality rate conditions. Unlike the extinction of species for the constant mortality, the nonconstant mortality may result in the coexistence of prey and predator for the predator-prey model with Allee effect.

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