Global asymptotic stability of a ratio-dependent predator-prey system with diffusion

被引：48
|
作者：
Fan, YH [1 ]
Li, WT
机构：
[1] NW Normal Univ, Coll Math & Informat Sci, Lanzhou 730070, Peoples R China
[2] Lanzhou Univ, Sch Math & Stat, Lanzhou 730000, Peoples R China
来源：
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2006年 / 188卷 / 02期
关键词：
upper and lower solutions; Lyapunov functions; predator-prey system;
D O I：
10.1016/j.cam.2005.04.007
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper is concerned with a predator-prey system with diffusion. The global asymptotic stability of the unique positive constant equilibrium is obtained under certain conditions. The Method used here is the upper and lower solutions combined with the monotone iteration and constructing suitable Lyapunov functions. (c) 2005 Elsevier B.V. All rights reserved.
引用
收藏
页码：205 / 227
页数：23
相关论文
共 50 条
  • [41] Spatiotemporal complexity of a ratio-dependent predator-prey system
    Wang, Weiming
    Liu, Quan-Xing
    Jin, Zhen
    PHYSICAL REVIEW E, 2007, 75 (05):
  • [42] Qualitative behaviour of a ratio-dependent predator-prey system
    Kovacs, Sandor
    Kiss, Krisztina
    Farkas, Miklos
    NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2009, 10 (03) : 1627 - 1642
  • [43] Bionomic exploitation of a ratio-dependent predator-prey system
    Maiti, Alakes
    Patra, Bibek
    Samanta, G. P.
    INTERNATIONAL JOURNAL OF MATHEMATICAL EDUCATION IN SCIENCE AND TECHNOLOGY, 2008, 39 (08) : 1061 - 1076
  • [44] Asymptotic dynamics and spatial patterns of a ratio-dependent predator-prey system with prey-taxis
    Cai, Yongli
    Cao, Qian
    Wang, Zhi-An
    APPLICABLE ANALYSIS, 2022, 101 (01) : 81 - 99
  • [45] 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
  • [46] Periodicity in a delayed ratio-dependent predator-prey system
    Fan, M
    Wang, K
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2001, 262 (01) : 179 - 190
  • [47] Global dynamics of a ratio-dependent Holling-Tanner predator-prey system
    Ding, Wei
    Huang, Wenzhang
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2018, 460 (01) : 458 - 475
  • [48] Stationary Patterns of a Ratio-Dependent Predator-Prey System with Cross-Diffusion
    Wang, Yu-Xia
    Li, Wan-Tong
    Shi, Hong-Bo
    MATHEMATICAL MODELLING AND ANALYSIS, 2011, 16 (03) : 461 - 474
  • [49] On the dynamics of an n-dimensional ratio-dependent predator-prey system with diffusion
    Duque, Cosme
    Kiss, Krisztina
    Lizana, Marcos
    APPLIED MATHEMATICS AND COMPUTATION, 2009, 208 (01) : 98 - 105
  • [50] Stability and Hopf bifurcation in a ratio-dependent predator-prey system with stage structure
    Xu, Rui
    Ma, Zhien
    CHAOS SOLITONS & FRACTALS, 2008, 38 (03) : 669 - 684
12345