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

被引：0
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作者：
Xiaoyuan Chang
Jimin Zhang
机构：
[1] Harbin University of Science and Technology,School of Applied Sciences
[2] Heilongjiang University,School of Mathematical Sciences
[3] Heilongjiang University,Heilongjiang Provincial Key Laboratory of the Theory and Computation of Complex Systems
来源：
Advances in Difference Equations | / 2019卷
关键词：
Leslie–Gower predator–prey system; Hopf bifurcation; Nonconstant positive solutions; Equilibrium; Ratio-dependent Holling III functional response; 92D25; 35K57;
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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.
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