Dynamics of a diffusive Leslie-Gower predator-prey system with ratio-dependent Holling III functional response

被引：5
|
作者：
Chang, Xiaoyuan [1 ]
Zhang, Jimin [2 ,3 ]
机构：
[1] Harbin Univ Sci & Technol, Sch Appl Sci, Harbin, Heilongjiang, Peoples R China
[2] Heilongjiang Univ, Sch Math Sci, Harbin, Heilongjiang, Peoples R China
[3] Heilongjiang Univ, Heilongjiang Prov Key Lab Theory & Computat Compl, Harbin, Heilongjiang, Peoples R China
来源：
ADVANCES IN DIFFERENCE EQUATIONS | 2019年 / 2019卷 / 1期
关键词：
Leslie-Gower predator-prey system; Hopf bifurcation; Nonconstant positive solutions; Equilibrium; Ratio-dependent Holling III functional response; 92D25; 35K57; STATIONARY PATTERNS; BIFURCATION-ANALYSIS; GLOBAL STABILITY; MODEL;
D O I：
10.1186/s13662-019-2018-3
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper is devoted to investigating the dynamics of a diffusive Leslie-Gower predator-prey system with ratio-dependent Holling III functional response. We first establish the stability of positive constant equilibrium, and show the condition under which system undergoes a Hopf bifurcation with the explicit computational formulas for determining the bifurcating properties. Especially, when the positive constant equilibrium loses its stability, a supercritical Hopf bifurcation with spatial homogeneous and stable bifurcating periodic solution occurs. Finally, we discuss the existence and nonexistence of nonconstant positive solutions with the help of Leray-Schauder degree theory and the implicit function theorem.
引用
收藏
页数：23
相关论文
共 50 条
12345