[1]王鲁欣,陈文彦.一类具有Holling-Ⅱ型响应函数的捕食模型定性分析[J].东南大学学报(自然科学版),2008,38(2):360-364.[doi:10.3969/j.issn.1001-0505.2008.02.035]
 Wang Luxin,Chen Wenyan.Qualitative analysis of a predator-prey model with Holling type Ⅱ functional response[J].Journal of Southeast University (Natural Science Edition),2008,38(2):360-364.[doi:10.3969/j.issn.1001-0505.2008.02.035]
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一类具有Holling-Ⅱ型响应函数的捕食模型定性分析()
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《东南大学学报(自然科学版)》[ISSN:1001-0505/CN:32-1178/N]

卷:
38
期数:
2008年第2期
页码:
360-364
栏目:
数学、物理学、力学
出版日期:
2008-03-20

文章信息/Info

Title:
Qualitative analysis of a predator-prey model with Holling type Ⅱ functional response
作者:
王鲁欣12 陈文彦1
1 东南大学数学系,南京 211189; 2 南通航运职业技术学院基础部, 南通 226010
Author(s):
Wang Luxin12 Chen Wenyan1
1 Department of Mathematics, Southeast University,Nanjing 211189, China
2 Basic Department, Nantong Shipping College, Nantong 226010, China
关键词:
捕食模型 稳定性 正平衡解
Keywords:
predator-prey model stability positive steady-states
分类号:
O175.26
DOI:
10.3969/j.issn.1001-0505.2008.02.035
摘要:
讨论具有Holling-Ⅱ型响应函数的捕食模型的齐次Neumann问题.首先通过构造上下解的方法研究了该问题半平凡解的全局稳定性,利用Lyapunov泛函和Routh-Hurwitz判定法分别讨论了正常数平衡解的全局稳定性和局部稳定性.其次给出了正平衡解的正的上下界的估计,以及非常数正平衡解的不存在性,最后利用拓扑度的方法研究了非常数正平衡解的存在性.
Abstract:
A predator-prey system with Holling type Ⅱ functional response under homogeneous Neumann boundary condition is considered.The globally asymptotically stability of semi-trivial solution to this system is firstly considered. Secondly, the globally asymptotically stability and locally asymptotically stability of the positive steady-states are discussed by constructing Lyapunov function and using Routh-Hurwitz theorem respectively.Then an priori estimates(positive upper and lower bounders)of positive steady-states is given. Finally, the existence of non-constant positive steady-states of the problem is obtained by using topology degree.

参考文献/References:

[1] Ko W,Ryu K.Qualitative analysis of a predator-prey model with Holling type Ⅱ functional responseincorporating a prey refuge[J]. J Differential Equations,2006,231(2):534-550.
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[3] Pang P Y H,Wang M X.Qualitative analysis of a ratio-dependent predator-prey system with diffusion[J].Proceeding of the Royal Society of Edinburgh,2003,133(4):919-942.
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备注/Memo

备注/Memo:
作者简介: 王鲁欣(1983—),女,硕士生; 陈文彦(联系人),女,博士,副教授,cwyseu@163.com.
基金项目: 国家自然科学基金资助项目(10601011).
引文格式: 王鲁欣,陈文彦.一类具有Holling-Ⅱ型响应函数的捕食模型的定性分析[J].东南大学学报:自然科学版,2008,38(2):360-364.
更新日期/Last Update: 2008-03-20