BIFURCATION ANALYSIS OF A DELAYED PREDATOR-PREY MODEL OF PREY MIGRATION AND PREDATOR SWITCHING

被引：10

作者：

Xu, Changjin ^{[1
,2
]}

Tang, Xianhua ^{[2
]}

Liao, Maoxin ^{[2
]}

机构：

[1] Guizhou Univ Finance & Econ, Sch Math & Stat, Guizhou Key Lab Econ Syst Simulat, Guiyang 550004, Peoples R China

[2] Cent S Univ, Sch Math Sci & Comp Technol, Changsha 410083, Hunan, Peoples R China

来源：

BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY | 2013年 / 50卷 / 02期

基金：

中国国家自然科学基金;

关键词：

predator-prey model; migration; switching; stability; Hopf bifurcation; GLOBAL STABILITY; HOPF-BIFURCATION; PERIODIC-SOLUTIONS; EPIDEMIC MODEL; DISPERSAL; SYSTEM; PERMANENCE; DIFFUSION; DYNAMICS;

D O I：

10.4134/BKMS.2013.50.2.353

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, a class of delayed predator-prey models of prey migration and predator switching is considered. By analyzing the associated characteristic transcendental equation, its linear stability is investigated and Hopf bifurcation is demonstrated. Some explicit formulae for determining the stability and the direction of the Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained by using the normal form theory and center manifold theory. Some numerical simulations for justifying the theoretical analysis are also provided. Finally, biological explanations and main conclusions are given.

引用

页码：353 / 373

页数：21

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