Dynamics of a modified Leslie-Gower predator-prey model with double Allee effects-Reference-Cited by-同舟云学术

Dynamics of a modified Leslie-Gower predator-prey model with double Allee effects

Published:2023 Issue:1 Volume:21 Page:792-831
ISSN:1551-0018
Container-title:Mathematical Biosciences and Engineering
language:
Short-container-title:MBE

Author:

Xing Mengyun¹,He Mengxin²,Li Zhong¹

Affiliation:

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

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

Abstract

<abstract><p>In this paper, we investigate the dynamic behavior of a modified Leslie-Gower predator-prey model with the Allee effect on both prey and predator. It is shown that the model has at most two positive equilibria, where one is always a hyperbolic saddle and the other is a weak focus with multiplicity of at least three by concrete example. In addition, we analyze the bifurcations of the system, including saddle-node bifurcation, Hopf bifurcation and Bogdanov-Takens bifurcation. The results show that the model has a cusp of codimension three and undergoes a Bogdanov-Takens bifurcation of codimension two. The system undergoes a degenerate Hopf bifurcation and has two limit cycles (the inner one is stable and the outer one is unstable). These enrich the dynamics of the modified Leslie-Gower predator-prey model with the double Allee effects.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

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

Reference30 articles.

1. P. H. Leslie, Some further notes on the use of matrices in population mathematics, Biometrika, 35 (1948), 213–245. https://doi.org/10.2307/2332342

2. P. H. Leslie, J. C. Gower, The properties of a stochastic model for the predator-prey type of interaction between two species, Biometrika, 47 (1960), 219–234. https://doi.org/10.2307/2333294

3. A. Korobeinikov, A Lyapunov function for Leslie-Gower predator-prey models, Appl. Math. Lett., 14 (2001), 697–699. https://doi.org/10.1016/s0893-9659(01)80029-x

4. S. B. Hsu, T. W. Huang, Global stability for a class of predator-prey systems, SIAM J. Appl. Math., 55 (1995), 763–783. https://doi.org/10.1137/s0036139993253201

5. T. Lindstrom, Qualitative analysis of a predator-prey system with limit cycles, J. Math. Biol., 31 (1993), 541–561. https://doi.org/10.1007/bf00161198

Cited by 1 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. Dynamic complexities in a predator–prey model with prey refuge influenced by double Allee effects;Mathematics and Computers in Simulation;2025-01