Stability and instability analysis for a ratio-dependent predator-prey system with diffusion effect

被引：20
作者：
Liao, Maoxin [1 ,2 ]
Tang, Xianhua [2 ]
Xu, Changjin [2 ,3 ]
机构：
[1] Univ S China, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China
[2] Cent S Univ, Sch Math Sci & Comp Technol, Changsha 410083, Hunan, Peoples R China
[3] Hunan Inst Engn, Coll Sci, Xiangtan 411104, Hunan, Peoples R China
来源：
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2011年 / 12卷 / 03期
关键词：
Ratio-dependent predator-prey system; Diffusion driven; Stability; Instability; Hopf bifurcation; Periodic solution; HOPF-BIFURCATION; MODEL;
D O I：
10.1016/j.nonrwa.2010.10.016
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we consider a ratio-dependent predator-prey system with diffusion. And we mainly discuss the following problems: (1) stability and Hopf bifurcation analysis of the positive equilibrium for the reduced ODE system; (2) Diffusion-driven instability of the equilibrium solution; (3) Hopf bifurcations for the corresponding diffusion system with homogeneous Neumann boundary conditions. In order to verify our theoretical results, some numerical simulations are also included, respectively. (C) 2010 Elsevier Ltd. All rights reserved.
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页码：1616 / 1626
页数：11
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