# [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] 点击复制 一类具有Holling-Ⅱ型响应函数的捕食模型定性分析() 分享到： var jiathis_config = { data_track_clickback: true };

38

2008年第2期

360-364

2008-03-20

## 文章信息/Info

Title:
Qualitative analysis of a predator-prey model with Holling type Ⅱ functional response

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):
1 Department of Mathematics, Southeast University,Nanjing 211189, China
2 Basic Department, Nantong Shipping College, Nantong 226010, China

Keywords:

O175.26
DOI:
10.3969/j.issn.1001-0505.2008.02.035

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.
[2] Peng R,Wang M X.Pattern formation in the Brusselator system[J]. J Math Anal Appl,2005,309:151-166.
[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.
[4] Nirenberg L.Topics in nonlinear functional analysis[M].New York:Courant Institute of Mathematical Sci-ence,1973.

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