Turing Instability and Bifurcation in a Diffusion Predator-Prey Model with Beddington-DeAngelis Functional Response

被引：10

作者：

Tan, Wei ^{[1
]}

Yu, Wenwu ^{[1
]}

Hayat, Tasawar ^{[2
]}

Alsaadi, Fuad ^{[3
]}

Fardoun, Habib M. ^{[4
]}

机构：

[1] Southeast Univ, Sch Math, Nanjing 211189, Jiangsu, Peoples R China

[2] Quaid I Azam Univ, Dept Math, Islamabad 45320, Pakistan

[3] King Abdulaziz Univ, Fac Engn, Dept Elect & Comp Engn, Jeddah 21589, Saudi Arabia

[4] King Abdulaziz Univ, Fac Comp & Informat Technol, Dept Informat Syst, Jeddah, Saudi Arabia

来源：

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2018年 / 28卷 / 09期

基金：

中国国家自然科学基金;

关键词：

Predator-prey model; diffusion; Turing instability; Hopf bifurcation; HOLLING TYPE; HOPF-BIFURCATION; SPATIOTEMPORAL PATTERNS; QUALITATIVE-ANALYSIS; COMPLEX PATTERNS; CROSS-DIFFUSION; EPIDEMIC MODEL; BIOLOGICAL-CONTROL; TIME-DELAY; SYSTEM;

D O I：

10.1142/S021812741830029X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we consider a predator-prey model with Beddington-DeAngelis functional response with or without diffusion. For this system, we give a complete and rigorous analysis of the dynamics including the existence of a global positive solution, the stability/Turing instability and the Hopf bifurcation. In the meanwhile, we show, via numerical simulations, that there appears Hopf bifurcation, steady state solution and Turing-Hopf bifurcation with the changes of some parameters of the system.

引用

页数：32

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