Bifurcations in a Predator-Prey Model of Leslie-Type with Simplified Holling Type IV Functional Response

被引：17

作者：

Zhang, Jun ^{[1
]}

Su, Juan ^{[2
]}

机构：

[1] Chengdu Univ Technol, Dept Math, Chengdu 610059, Sichuan, Peoples R China

[2] Chengdu Normal Univ, Dept Math, Chengdu 611130, Sichuan, Peoples R China

来源：

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2021年 / 31卷 / 04期

关键词：

Predator– prey model of Leslie-type; Hopf bifurcation; Bogdanov– Takens bifurcation; resultant elimination; SYSTEM; STABILITY;

D O I：

10.1142/S0218127421500541

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we complete the remaining investigation of local bifurcations in a predator-prey model of Leslie-type with simplified Holling type IV functional response. The system has at most three equilibria, and local bifurcations were completely investigated in the cases of one and three equilibria, but in the case of two equilibria the previous study was only on a fixed parameter. We extend the study in the case of two equilibria for all parameters, and find that the system exhibits Hopf bifurcations of codimensions 1 and 2, and Bogdanov-Takens bifurcations of codimensions 2 and 3. Previous results and our research show that the codimension of local bifurcations is at most 3, and both focus type and cusp type Bogdanov-Takens bifurcations of codimension 3 can occur.

引用

页数：17

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