Stability and Hopf bifurcation of a delayed reaction-diffusion predator-prey model with anti-predator behaviour

被引：17

作者：

Liu, Jia ^{[1
]}

Zhang, Xuebing ^{[2
]}

机构：

[1] Huaian Vocat Coll Informat Technol, Dept Basic Courses, Huaian 223003, Peoples R China

[2] Nanjing Univ Informat Sci & Technol, Coll Math & Stat, Nanjing 210044, Jiangsu, Peoples R China

来源：

NONLINEAR ANALYSIS-MODELLING AND CONTROL | 2019年 / 24卷 / 03期

关键词：

delay; stability; Hopf bifurcation; anti-predator; FOOD-CHAIN MODEL; TIME-DELAY; DYNAMICS; SYSTEM; COMPETITION; RISK;

D O I：

10.15388/NA.2019.3.5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the dynamics of a delayed reaction-diffusion predator-prey model with anti-predator behaviour. By using the theory of partial functional differential equations, Hopf bifurcation of the proposed system with delay as the bifurcation parameter is investigated. It reveals that the discrete time delay has a destabilizing effect in the model, and a phenomenon of Hopf bifurcation occurs as the delay increases through a certain threshold. By utilizing upper-lower solution method, the global asymptotic stability of the interior equilibrium is studied. Finally, numerical simulation results are presented to validate the theoretical analysis.

引用

页码：387 / 406

页数：20

共 36 条

[1] EFFECTS OF ADAPTIVE PREDATORY AND ANTIPREDATOR BEHAVIOR IN A 2-PREY ONE-PREDATOR SYSTEM [J].

ABRAMS, P ;

MATSUDA, H .

EVOLUTIONARY ECOLOGY, 1993, 7 (03) :312-326

[2]

[Anonymous], 1992, NONLINEAR PARABOLIC, DOI DOI 10.1007/978-1-4615-3034-3

[3] Complex Dynamics of a host parasite model with both horizontal and vertical transmissions in a spatial heterogeneous environment [J].

Cai, Yongli ;

Kang, Yun ;

Banerjee, Malay ;

Wang, Weiming .

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2018, 40 :444-465

[4] Hopf bifurcation and optimal control in a diffusive predator-prey system with time delay and prey harvesting [J].

Chang, Xiaoyuan ;

Wei, Junjie .

NONLINEAR ANALYSIS-MODELLING AND CONTROL, 2012, 17 (04) :379-409

[5] THE EFFECT OF DELAYS ON THE PERMANENCE FOR LOTKA-VOLTERRA SYSTEMS [J].

CHEN, LS ;

LU, ZY ;

WANG, WD .

APPLIED MATHEMATICS LETTERS, 1995, 8 (04) :71-73

[6] A note on Hopf bifurcations in a delayed diffusive Lotka-Volterra predator-prey system [J].

Chen, Shanshan ;

Shi, Junping ;

Wei, Junjie .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2011, 62 (05) :2240-2245

[7] Predator-prey role reversals, juvenile experience and adult antipredator behaviour [J].

Choh, Yasuyuki ;

Ignacio, Maira ;

Sabelis, Maurice W. ;

Janssen, Arne .

SCIENTIFIC REPORTS, 2012, 2

[8] ANTIPREDATOR BEHAVIOR AND THE POPULATION-DYNAMICS OF SIMPLE PREDATOR-PREY SYSTEMS [J].

IVES, AR ;

DOBSON, AP .

AMERICAN NATURALIST, 1987, 130 (03) :431-447

[9]

Li Z., 1990, REGIONAL C SERIES AP

[10]

Lima SL, 1998, ADV STUD BEHAV, V27, P215

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