Dynamical analysis of a two species amensalism model with Beddington-DeAngelis functional response and Allee effect on the second species

被引：61

作者：

Guan, Xinyu ^{[1
]}

Chen, Fengde ^{[1
]}

机构：

[1] Fuzhou Univ, Coll Math & Comp Sci, Fuzhou 350116, Fujian, Peoples R China

来源：

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2019年 / 48卷

基金：

中国国家自然科学基金;

关键词：

Amensalism model; Beddington-DeAngelis functional response; Allee effect; Bifurcation; Global dynamics; PREDATOR-PREY SYSTEM; BIFURCATION-ANALYSIS; MUTUAL INTERFERENCE; PERIODIC-SOLUTIONS; STAGE STRUCTURE; STABILITY;

D O I：

10.1016/j.nonrwa.2019.01.002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A two species amensalism model with Beddington DeAngelis functional response is proposed and studied in this paper. The existence and stability of possible equilibria are investigated. Under some additional assumptions, there are two stable equilibria which implies this system is not asymptotically stable. Based on the stability analysis of equilibria, closed orbits and the saddle connection, we give some comprehensive bifurcation and global dynamics of the system. Next, we further incorporate the Allee effect into the second species and provide a complete qualitative and bifurcation analysis of the system with Allee effect. Numerical simulations show that the system with an Allee effect must take a longer time to reach its stable steady-state solution than that without Allee effect. There is a good agreement between the present results and the numeric simulations. (C) 2019 Elsevier Ltd. All rights reserved.

引用

页码：71 / 93

页数：23

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