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.
引用
收藏
页码：1616 / 1626
页数：11
相关论文
共 50 条
  • [1] Qualitative analysis of a ratio-dependent predator-prey system with diffusion
    Pang, PYH
    Wang, MX
    PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2003, 133 : 919 - 942
  • [2] Global stability analysis of a ratio-dependent predator-prey system
    Tie-jun Lu
    Mei-juan Wang
    Yan Liu
    Applied Mathematics and Mechanics, 2008, 29 : 495 - 500
  • [3] ANALYSIS OF STABILITY FOR A DISCRETE RATIO-DEPENDENT PREDATOR-PREY SYSTEM
    Chen, Guangye
    Teng, Zhidong
    Hu, Zengyun
    INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 2011, 42 (01): : 1 - 26
  • [4] Global stability analysis of a ratio-dependent predator-prey system
    鲁铁军
    王美娟
    刘妍
    AppliedMathematicsandMechanics(EnglishEdition), 2008, (04) : 495 - 500
  • [5] Analysis of stability for a discrete ratio-dependent predator-prey system
    Guangye Chen
    Zhidong Teng
    Zengyun Hu
    Indian Journal of Pure and Applied Mathematics, 2011, 42 : 1 - 26
  • [6] Global asymptotic stability of a ratio-dependent predator-prey system with diffusion
    Fan, YH
    Li, WT
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2006, 188 (02) : 205 - 227
  • [7] Turing instability for a ratio-dependent predator-prey model with diffusion
    Aly, Shaban
    Kim, Imbunm
    Sheen, Dongwoo
    APPLIED MATHEMATICS AND COMPUTATION, 2011, 217 (17) : 7265 - 7281
  • [8] Global stability analysis of a ratio-dependent predator-prey system
    Lu Tie-jun
    Wang Mei-juan
    Liu Yan
    APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION, 2008, 29 (04) : 495 - 500
  • [9] Note on a ratio-dependent predator-prey system with diffusion
    Peng, R
    Wang, MX
    NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2006, 7 (01) : 1 - 11
  • [10] An impulsive ratio-dependent predator-prey system with diffusion
    Akhmet, M. U.
    Beklioglu, M.
    Ergenc, T.
    Tkachenko, V. I.
    NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2006, 7 (05) : 1255 - 1267
12345