Analysis of modified Holling-Tanner model with strong Allee effect

Kunlun Huang; Xintian Jia; Cuiping Li; Kunlun Huang; Xintian Jia; Cuiping Li

doi:10.3934/mbe.2023693

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 8: 15524-15543. doi: 10.3934/mbe.2023693

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Analysis of modified Holling-Tanner model with strong Allee effect

LMIB-School of Mathematical Sciences, Beihang University, Beijing 100083, China

Academic Editor: Xiang-Sheng Wang

Received: 13 May 2023 Revised: 20 July 2023 Accepted: 20 July 2023 Published: 26 July 2023

In this paper, we study a predator-prey system, the modified Holling-Tanner model with strong Allee effect. The existence and stability of the non-negative equilibria are discussed first. Several kinds of bifurcation phenomena, which the model may undergo, such as saddle-node bifurcation, Hopf bifurcation, and Bogdanov-Takens bifurcation, are studied second. Bifurcation diagram for Bogdanov-Takens bifurcation of codimension 2 is given. Then, possible dynamical behaviors of this model are illustrated by numerical simulations. This paper appears to be the first study of the modified Holling-Tanner model that includes the influence of a strong Allee effect.
- Holling-Tanner model,
- strong Allee effect,
- Bogdanov-Takens bifurcation,
- codimension,
- coexistence
Citation: Kunlun Huang, Xintian Jia, Cuiping Li. Analysis of modified Holling-Tanner model with strong Allee effect[J]. Mathematical Biosciences and Engineering, 2023, 20(8): 15524-15543. doi: 10.3934/mbe.2023693

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Abstract

In this paper, we study a predator-prey system, the modified Holling-Tanner model with strong Allee effect. The existence and stability of the non-negative equilibria are discussed first. Several kinds of bifurcation phenomena, which the model may undergo, such as saddle-node bifurcation, Hopf bifurcation, and Bogdanov-Takens bifurcation, are studied second. Bifurcation diagram for Bogdanov-Takens bifurcation of codimension 2 is given. Then, possible dynamical behaviors of this model are illustrated by numerical simulations. This paper appears to be the first study of the modified Holling-Tanner model that includes the influence of a strong Allee effect.

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