Bifurcation analysis in a Holling-Tanner predator-prey model with strong Allee effect-Reference-Cited by-同舟云学术

Bifurcation analysis in a Holling-Tanner predator-prey model with strong Allee effect

Published:2023 Issue:5 Volume:20 Page:8632-8665
ISSN:1551-0018
Container-title:Mathematical Biosciences and Engineering
language:
Short-container-title:MBE

Author:

Liu Yingzi¹,Li Zhong¹,He Mengxin²

Affiliation:

1. School of Mathematics and Statistics, Fuzhou University, Fuzhou, Fujian 350108, PR China

2. College of Mathematics and Data Science, Minjiang University, Fuzhou, Fujian 350108, PR China

Abstract

<abstract><p>In this paper, we analyze the bifurcation of a Holling-Tanner predator-prey model with strong Allee effect. We confirm that the degenerate equilibrium of system can be a cusp of codimension 2 or 3. As the values of parameters vary, we show that some bifurcations will appear in system. By calculating the Lyapunov number, the system undergoes a subcritical Hopf bifurcation, supercritical Hopf bifurcation or degenerate Hopf bifurcation. We show that there exists bistable phenomena and two limit cycles. By verifying the transversality condition, we also prove that the system undergoes a Bogdanov-Takens bifurcation of codimension 2 or 3. The main conclusions of this paper complement and improve the previous paper <sup>[<xref ref-type="bibr" rid="b30">30</xref>]</sup>. Moreover, numerical simulations are given to verify the theoretical results.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

Applied Mathematics,Computational Mathematics,General Agricultural and Biological Sciences,Modeling and Simulation,General Medicine

Reference39 articles.

1. S. X. Yan, D. X. Jia, T. H. Zhang, S. L. Yuan, Pattern dynamic in a diffusive predator-prey model with hunting cooperations, Chaos Solitons Fract., 130 (2020), 109428. https://doi.org/10.1016/j.chaos.2019.109428

2. D. Tang, Y. M. Chen, Predator-prey systems in open advective heterogeneous environments with Holling-Tanner interaction term, J. Differ. Equations, 334 (2022), 280–308. https://doi.org/10.1016/j.jde.2022.06.022

3. W. Ding, W. Z. Huang, Global dynamics of a ratio-dependent Holling-Tanner predator-prey system, J. Math. Anal. Appl., 460 (2018), 458–475. https://doi.org/10.1016/j.jmaa.2017.11.057

4. S. L. Yuan, D. M. Wu, G. J. Lan, H. Wang, Noise-induced transitions in a nonsmooth predator-prey model with stoichiometric constraints, Bull. Math. Biol., 55 (2020), 2250086. https://doi.org/10.1007/s11538-020-00733-y

5. S. Q. Zhang, T. H. Zhang, S. L. Yuan, Dynamics of a stochastic predator-prey model with habitat complexity and prey aggregation, Ecol. Compl., 45 (2021), 100889. https://doi.org/10.1016/j.ecocom.2020.100889

Cited by 5 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Sustainable management of predatory fish affected by an Allee effect through marine protected areas and taxation;Mathematical Biosciences;2024-07

2. Zero Hopf Bifurcation and Chaotic Behavior in a Leslie Tritrophic Model;International Journal of Applied and Computational Mathematics;2023-10-13

3. Dynamics of a modified Leslie-Gower predator-prey model with double Allee effects;Mathematical Biosciences and Engineering;2023

4. Stability and bifurcation analysis of a two-patch model with the Allee effect and dispersal;Mathematical Biosciences and Engineering;2023

5. Sustainable Management of Predatory Fish Affected by an Allee Effect Through Marine Protected Areas Andtaxation;2023