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具有避难所的捕食-食饵模型的全局分歧 被引量：4

Global bifurcation of a predator-prey system incorporating a prey refuge
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摘要 研究了一类具有避难所的两物种间的捕食-食饵模型,其功能反应函数为HollingⅢ型。主要利用分歧理论,结合极值原理,得到系统非常数正解的存在性。在一维情况下,对于非常数正解的全局分歧结构给出了细节的描述。 A predator-prey system between two species with Holling type Ⅲ functional response incorporating a prey refuge was discussed. The existence of positive steady-state solutions was derived mainly through the global bifurcation and the maximum principle of elliptic equations. In a one dimensional ease, a detailed description for the global bifurcation of the set of the nonconstant steady states was given.
作者 张丽娜 李艳玲 解玉龙
机构地区 陕西师范大学数学与信息科学学院
出处 《山东大学学报（理学版）》 CAS CSCD 北大核心 2007年第12期110-115,共6页 Journal of Shandong University(Natural Science)
基金 国家自然科学基金资助项目(10571115)
关键词 避难所 HollingⅢ型 极值原理 全局分歧 prey refuge Holling type Ⅲ maximum principle global bifurcation
分类号 O175.26 [理学—基础数学]
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参考文献11

  • 1HOLLING C S. The functional response of predator to prey density and its role in minicry and population regulation[J]. Men Ent Soc Can, 1965, 45:1-60.
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  • 6KAR T K. Stability analysis of a prey-predator model incorporating a prey refuge[J]. Commun Nonlinear Sci Numer Simul, 2005, 10: 581-691.
  • 7HUANG Y J, CHEN F D, ZHONG L. Stability analysis of a prey-predator model with Holling type Ⅲ response function incorporating a prey refuge[J]. Appl Math Comput, 2006, 182:672-683.
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共引文献22

同被引文献32

  • 1Yan Lv,Wei Lv,Jian-hua Sun.Existence of Positive Periodic Solutions for Nonautonomous Predator-prey Systems with Discrete and Continuously Distributed Delays[J].Acta Mathematicae Applicatae Sinica,2007,23(1):39-48. 被引量：3
  • 2HUANG Y J,- CHEN F D, ZHONG L. Stability analysis of a prey-predator model with Holling Ⅲ response function incorporating a prey refuge[J]. Appl Math Comput, 2006, 182:672-683.
  • 3CHEN J P, ZHANG H D. The qualitative analysis of two species predator-prey model with Holling's type Ⅲ functional response[J]. Appl Math Mech, 1986, 1:73-80.
  • 4HAUSRATH A. Analysis of a model predator-prey system with refuges[J]. J Math Anal Appl, 1994, 181:531-545.
  • 5KAR T K. Stability analysis of a prey-predator model incorporating a prey refuge[J]. Commun Nonlinear Sci Numer Simul, 2005, 10: 681-691.
  • 6WANG M X. Non-constant positive steady-states of the Sel' kov model[J]. J Differential Equations, 2003, 190:60)-620.
  • 7MCGOUGH J S, KILEY K. Pattern formation in the Gray-Scott model[J]. Nonlinear Anal, Real World Appl, 2004, 5:105-121.
  • 8PENG R, WANG M X. Pattern formation in the Brusselator system[J]. J Math Anal Appl, 2005, 309:151-166.
  • 9PANG P Y H, WANG M X. Qualitative analysis of a ratio-dependent predator-prey system with diffusion[J]. Proc Roy Soc Edinburgh A, 2003, 133(4) :919-942.
  • 10ZENG X Z. Non-constant positive steady-states of a prey-predator system with cross-diffusions[J]. J Math Anal Appl, 2007, 332:989-1009.

引证文献4

二级引证文献14

山东大学学报（理学版）
2007年 第12期

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