Dynamic behaviors of a nonautonomous predator-prey system with Holling type II schemes and a prey refuge

被引：9

作者：

Wu, Yumin ^{[1
]}

Chen, Fengde ^{[2
]}

Du, Caifeng ^{[3
]}

机构：

[1] China Univ Petr, Shengli Coll, Sch Basic Sci, Dongying 257061, Shandong, Peoples R China

[2] Fuzhou Univ, Coll Math & Comp Sci, Fuzhou 350014, Fujian, Peoples R China

[3] China Univ Petr, Shengli Coll, Teaching Affairs Off, Dongying 257061, Shandong, Peoples R China

来源：

ADVANCES IN DIFFERENCE EQUATIONS | 2021年 / 2021卷 / 01期

关键词：

Predator-prey; Permanence; Holling type II; Global stability; Refuge; HOPF-BIFURCATION; STAGE STRUCTURE; MODEL; STABILITY; DELAY;

D O I：

10.1186/s13662-021-03222-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider a nonautonomous predator-prey model with Holling type II schemes and a prey refuge. By applying the comparison theorem of differential equations and constructing a suitable Lyapunov function, sufficient conditions that guarantee the permanence and global stability of the system are obtained. By applying the oscillation theory and the comparison theorem of differential equations, a set of sufficient conditions that guarantee the extinction of the predator of the system is obtained.

引用

页数：15

共 33 条

[1]

Amant J., 1970, THESIS U CALIF SANTA

[2] THE ORIGINS AND EVOLUTION OF PREDATOR PREY THEORY [J].

BERRYMAN, AA .

ECOLOGY, 1992, 73 (05) :1530-1535

[3]

Chen F.D., 2012, DISCRETE DYN NAT SOC, V2012

[4] Stability of the boundary solution of a nonautonomous predator-prey system with the Beddington-DeAngelis functional response [J].

Chen, Fengde ;

Chen, Yuming ;

Shi, Jinlin .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 344 (02) :1057-1067

[5] Note on the permanence of a competitive system with infinite delay and feedback controls [J].

Chen, Fengde ;

Li, Zhong ;

Huang, Yunjin .

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2007, 8 (02) :680-687

[6]

Chen FD, 2017, J MATH COMPUT SCI-JM, V17, P266, DOI 10.22436/jmcs.017.02.08

[7] Global asymptotical stability of the positive equilibrium of the Lotka-Volterra prey-predator model incorporating a constant number of prey refuges [J].

Chen, Fengde ;

Ma, Zhaozhi ;

Zhang, Huiying .

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2012, 13 (06) :2790-2793

[8]

Chen J.H., 2018, ANN APPL MATH, V34, P32

[9]

[陈柳娟 Chen Liujuan], 2014, [数学学报, Acta Mathematica Sinica], V57, P301

[10] Qualitative analysis of a predator-prey model with Holling type II functional response incorporating a constant prey refuge [J].

Chen, Liujuan ;

Chen, Fengde ;

Chen, Lijuan .

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2010, 11 (01) :246-252

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