Stability and Bifurcation Analysis on a Predator-Prey System with the Weak Allee Effect

被引：12
|
作者：
Zhang, Jianming [1 ]
Zhang, Lijun [2 ]
Bai, Yuzhen [3 ]
机构：
[1] Zhejiang Sci Tech Univ, Sch Sci, Dept Math, Hangzhou 310018, Zhejiang, Peoples R China
[2] Shandong Univ Sci & Technol, Coll Math & Syst Sci, Qingdao 266590, Shandong, Peoples R China
[3] Qufu Normal Univ, Sch Math Sci, Qufu 273165, Peoples R China
来源：
MATHEMATICS | 2019年 / 7卷 / 05期
关键词：
weak Allee effect; predator-prey system; Hopf bifurcations; stability switches; SPATIOTEMPORAL DYNAMICS; MODEL;
D O I：
10.3390/math7050432
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, the dynamics of a predator-prey system with the weak Allee effect is considered. The sufficient conditions for the existence of Hopf bifurcation and stability switches induced by delay are investigated. By using the theory of normal form and center manifold, an explicit expression, which can be applied to determine the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions, are obtained. Numerical simulations are performed to illustrate the theoretical analysis results.
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页数：15
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