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一个具有时滞和阶段结构的捕食-被捕食模型

A Stage-Structured Predator-Prey Model with Time Delays
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摘要 研究一个具有时滞和阶段结构的捕食-被捕食模型.运用函数极限方法证明了相应文献中的结论在更弱的条件下也成立,从而得到了保证该生态系统持续生存与绝灭的充分性条件. A delay predator-prey model with stage structure for prey is investigated. By using the limit of function , the conlusions of relative article are proved essentially and they hold in weaker conditions. A set of easily verifiable sufficient conditions are derived for the permanence and extinction of the proposed ecological system.
作者 王锐利 赵永华 毕卫萍
机构地区 济源职业技术学院基础部 河南师范大学数学与信息科学学院
出处 《河南师范大学学报（自然科学版）》 CAS CSCD 北大核心 2009年第3期15-18,共4页 Journal of Henan Normal University(Natural Science Edition)
基金 河南省教育厅自然科学基金(2007120005)
关键词 阶段结构 捕食者-食饵模型 时滞 永久持续生存 绝灭 stage structure predator-prey model time delays permanence extinction
分类号 O175 [理学—基础数学]
  • 相关文献

参考文献9

  • 1徐瑞,郝飞龙,陈兰荪.一个具有时滞和阶段结构的捕食-被捕食模型[J].数学物理学报（A辑）,2006,26(3):387-395. 被引量：30
  • 2Goh B S. Global stability in two species interactions[J]. J Math Bio1,1976, 3(3/4) :313--318.
  • 3Hastings A. Global stability in two species systems[J].J Math Bio1,1978,5(4):399--403.
  • 4He X Z. Stability and delays in a predator-prey syste[J].J Math Anal Appl,1996,198(2):355--370.
  • 5Ma Z. Mathematical Modeling and Research in Ecology[M]. Hefei: Anhui Educational Publishing House,1996:25--26.
  • 6Cushing J M. Integrodifferential Equations and Delay Models in Population Dynamies[M]. Heidelberg: Springer,1979:13--70.
  • 7Kuang Y. Delay Differential Equations with Applications in Population Dynamics[M]. New York: Academic Press, 1993: 302--309.
  • 8Wang W, Ma Z. Harmless delays for uniform persistence[J].J Math Anal Appl,1991,158(1):256--268.
  • 9Hale J. Theory of Functions Differential Equations[M]. Heidelberg: Springer-Verlag,1977:36-56.

二级参考文献15

  • 1Goh B S. Global stability in two species interactions. J Math Biol, 1976, 3(3-4): 313-318
  • 2Hastings A. Global stability in two species systems. J Math Biol, 1978, 5(4): 399-403
  • 3He X Z. Stability and delays in a predator-prey system. J Math Anal Appl, 1996, 198(2): 355-370
  • 4Aièllo W G, Freedman H I. A time delay model of single-species growth with stage structure. Math Biosci,1990, 101(2): 139-153
  • 5Aiello W G, Freedman H I, Wu J. Analysis of a model representing stage-structured population growth with state-dependent time delay. SIAM J Appl Math, 1992, 52(3): 855- 869
  • 6Wang W, Chen L. A predator-prey system with stage structure for predator. Comput Maria Appl, 1997,33(8): 83 -91
  • 7Magnusson K G, Destabilizing effect of cannibalism on a structured predator-prey system. Math Biosci,1999, 155(1): 61-75
  • 8Zhang X, Chen L, Neumann A U. The stage-structured predator-prey model and optimal havesting policy.Math Biosci, 2000, 168(2): 201- 210
  • 9Ma Z. Mathematical Modeling and Research in Ecology. Hefei: Anhui Educational Publishing House,1996. 25- 26
  • 10Cushing J M. Integrodifferential Equations and Delay Models in Population Dynamics. Lecture Notes in Biomathematics 20. Heidelberg, Springer, 1979. 13-70

共引文献29

河南师范大学学报（自然科学版）
2009年 第3期

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