DYNAMIC STUDY OF A PREDATOR-PREY MODEL WITH WEAK ALLEE EFFECT AND HOLLING TYPE-III FUNCTIONAL RESPONSE

被引：4

作者：

Liu, Hua ^{[1
]}

Ye, Yong ^{[1
]}

Wei, Yumei

Ma, Ming ^{[1
]}

Ye, Jianhua ^{[1
]}

机构：

[1] Northwest Minzu Univ, Sch Math & Comp Sci, Lanzhou 730030, Gansu, Peoples R China

来源：

DYNAMIC SYSTEMS AND APPLICATIONS | 2018年 / 27卷 / 04期

基金：

中国国家自然科学基金;

关键词：

weak Allee effect; prey-predator; stability; Hopf bifurcation; BIFURCATION-ANALYSIS; STABILITY; SYSTEM;

D O I：

10.12732/dsa.v27i4.15

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A prey-predator model with weak Allee effect in prey growth, Holling type-III functional response in predator growth is proposed and its dynamical behaviors are studied in detail. The existence, boundness and stability of the equilibria are qualitatively discussed. Hopf bifurcation analysis are also taken into account. We present some numerical simulations to illustrate our theoretical analysis. Through computer simulation, we found the position of each equilibrium point in the phase diagram that we drew. In the bifurcation diagram we found the threshold for undergoing Hopf bifurcation.

引用

页码：943 / 953

页数：11

共 14 条

[1] Global dynamics of a modified Leslie-Gower predator-prey model with Crowley-Martin functional responses [J].

Ali N. ;

Jazar M. .

Journal of Applied Mathematics and Computing, 2013, 43 (1-2) :271-293

[2]

[Anonymous], tures in a 2D exponential diffeomorphism with Allee

[3]

Aziz-Alaoui M. A., 2011, APPL MATH COMPUT, V217, P9085

[4] Study of a Leslie-Gower-type tritrophic population model [J].

Aziz-Alaoui, MA .

CHAOS SOLITONS & FRACTALS, 2002, 14 (08) :1275-1293

[5] Maturation delay for the predators can enhance stable coexistence for a class of prey-predator models [J].

Banerjee, Malay ;

Takeuchi, Yasuhiro .

JOURNAL OF THEORETICAL BIOLOGY, 2017, 412 :154-171

[6]

Caughley G., 1981, Theoretical ecology, principles and applications, P132

[7]

CHENG KS, 1981, J MATH BIOL, V12, P115, DOI 10.1007/BF00275207

[8]

Freedman HI., 1980, BIOMETRICS, V22, P219

[9] Bifurcation analysis of modified Leslie-Gower predator-prey model with Michaelis-Menten type prey harvesting [J].

Gupta, R. P. ;

Chandra, Peeyush .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2013, 398 (01) :278-295

[10] Ratio-Dependent Predator-Prey Models of Interacting Populations [J].

Haque, Mainul .

BULLETIN OF MATHEMATICAL BIOLOGY, 2009, 71 (02) :430-452

← 1 2 →