Bifurcations in a Diffusive Predator-Prey Model with Beddington-DeAngelis Functional Response and Nonselective Harvesting

被引：9

作者：

Sun, Xiuli ^{[1
]}

Yuan, Rong ^{[2
]}

Wang, Luan ^{[3
]}

机构：

[1] Taiyuan Univ Technol, Coll Math, Taiyuan 030024, Shanxi, Peoples R China

[2] Beijing Normal Univ, Sch Math Sci, Beijing 100875, Peoples R China

[3] Shanxi Univ Finance & Econ, Fac Econ, Taiyuan 030006, Shanxi, Peoples R China

来源：

JOURNAL OF NONLINEAR SCIENCE | 2019年 / 29卷 / 01期

关键词：

Bifurcation; Lyapunov-Schmidt reduction; Beddington-DeAngelis functional response; Nonselective harvesting; Reaction-diffusion; HOPF-BIFURCATION; STABILITY; EQUATIONS; PATTERNS; SYSTEM;

D O I：

10.1007/s00332-018-9487-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we discuss the dynamics of a predator-prey model with Beddington-DeAngelis functional response and nonselective harvesting. By using the Lyapunov-Schmidt reduction, we obtain the existence of spatially nonhomogeneous steady-state solution. The stability and existence of Hopf bifurcation at the spatially nonhomogeneous steady-state solution with the change of a specific parameter are investigated by analyzing the distribution of the eigenvalues. We also get an algorithm for determining the bifurcation direction of the Hopf bifurcating periodic solutions near the nonhomogeneous steady-state solution. Finally, we show some numerical simulations to verify our analytical results.

引用

页码：287 / 318

页数：32

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