QUALITATIVE STRUCTURE OF A DISCRETE PREDATOR-PREY MODEL WITH NONMONOTONIC FUNCTIONAL RESPONSE

被引：4

作者：

Zhang, Yanlin ^{[1
]}

Cheng, Qi ^{[2
]}

Deng, Shengfu ^{[2
]}

机构：

[1] Minnan Sci & Technol Univ, Quanzhou 362332, Fujian, Peoples R China

[2] Huaqiao Univ, Sch Math Sci, Quanzhou 362021, Fujian, Peoples R China

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S | 2023年 / 16卷 / 3-4期

基金：

中国国家自然科学基金;

关键词：

Blowing-up method; normal form; degenerate fixed point; discrete predator-prey model; nonmonotonic functional response; BIFURCATION; SYSTEM; CHAOS;

D O I：

10.3934/dcdss.2022065

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the qualitative structure of a discrete predator-prey model with nonmonotonic functional response near a degenerate fixed point whose eigenvalues are +/- 1. Firstly, the model is transformed into an ordinary differential system by using the normal form theory and the Takens's theorem. Then, the qualitative properties of this ordinary differential system near the degenerate equilibrium are analyzed with the blowing-up method. Finally, according to the conjugacy between the discrete model and the time-one mapping of the vector field, the qualitative structure of this discrete model is obtained. Numerical simulations are also given.

引用

页码：773 / 786

页数：14

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