Dynamics of a Leslie-Gower predator-prey system with cross-diffusion

被引：4
|
作者：
Zou, Rong [1 ]
Guo, Shangjiang [2 ]
机构：
[1] Guangxi Univ Finance & Econ, Sch Informat & Stat, Nanning 530003, Peoples R China
[2] China Univ Geosci, Sch Math & Phys, Wuhan 430074, Peoples R China
来源：
ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS | 2020年 / 65期
关键词：
cross-diffusion; predator-prey system; global existence; stability; Hopf bifurcation; Bogdanov-Takens bifurcation; SPATIOTEMPORAL PATTERNS; GLOBAL EXISTENCE; BIFURCATION; MODEL; BOUNDEDNESS; STABILITY;
D O I：
10.14232/ejqtde.2020.1.65
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A Leslie-Gower predator-prey system with cross-diffusion subject to Neumann boundary conditions is considered. The global existence and boundedness of solutions are shown. Some sufficient conditions ensuring the existence of nonconstant solutions are obtained by means of the Leray-Schauder degree theory. The local and global stability of the positive constant steady-state solution are investigated via eigenvalue analysis and Lyapunov procedure. Based on center manifold reduction and normal form theory, Hopf bifurcation direction and the stability of bifurcating timeperiodic solutions are investigated and a normal form of Bogdanov-Takens bifurcation is determined as well.
引用
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页码：1 / 33
页数：33
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