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系数含时滞的阶段结构捕食模型的稳定性 被引量：1

Stability of Stage Structured Predator-prey Model with Delay Dependent Parameters
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摘要 研究一类系数含时滞的阶段结构捕食系统,分析了平衡点的局部稳定性,给出了边界平衡点(1,0)全局渐近稳定的充要条件和系统一致持续生存的充分条件,证明了正平衡点局部渐近稳定则全局渐近稳定的结论. A class of stage structured predator-prey model with delay dependent parameters was studied.After local stability of equilibriums point being analyzed,accompanied by sufficient condition for system＇s uniform persistence,necessary and sufficient conditions for the global asymptotical stability of the boundary equilibrium（1,0） were given.Results showed that the locally asymptotically stable in positive equilibrium point decides the global asymptotical stability.
作者 胡宝安 刘俊峰 李亚玲
机构地区 军事交通学院基础部
出处 《温州大学学报（自然科学版）》 2012年第2期1-7,共7页 Journal of Wenzhou University(Natural Science Edition)
关键词 阶段结构捕食模型 时滞 稳定性 Stage Structured Predator-prey Model Delay Stability
分类号 O175.14 [理学—基础数学]
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参考文献6

  • 1Wang W D,Chen L S. A Predator-prey System with Stage-structure for Predator[J].Computers and Mathematics with Applications,1997.83-91.doi:10.1016/S0898-1221(97)00056-4.
  • 2Aiello W G,Freedman H I. A time-delay model of single species growth with stage structure[J].Mathematical Biosciences,1990.139-153.doi:10.1016/0025-5564(90)90019-U.
  • 3Gourley S A,Kuang Y. A stage structured predator-prey model and its dependence on maturation delay and death rate[J].Journal of Mathematical Biology,2004.188-200.
  • 4Bereua E,Kuang Y. Geometric stability switch criteria in delay differential systems with delay dependent parameters[J].SIAM Journal on Mathematical Analysis,2002.1144-1165.
  • 5Xiao Y N,Chen L S. Modeling and analysis of a predator-prey model with disease in the prey[J].Mathematical Biosciences,2001.59-82.
  • 6Kuang Y. Delay Differential Equations with Applications in Population Dynamics[M].Boston:academic Press,1993.

同被引文献11

  • 1胡宝安,陈博文,夏爱生,邹晓建,鞠涛.Logistic增长的时滞SIS模型分析[J].工程数学学报,2007,24(2):373-376. 被引量：6
  • 2Richards F J. A Flexible Growth Function for Empirical Use[J]. J Exp Biol, 1959,10:290 - 300.
  • 3Yang Yiqun, Wu Lianghuan, Wu Jimiao. on the Richards Curve [ J ]. J Biomath ,2000,15 (4) : 85 - 387.
  • 4Wang W D, Chen L S. A Predator-prey System with Stage-structure for Predator [ J]. Computers Math Applic, 1997,8:83-91.
  • 5Tian Xiaohong, Xu Rui. Hopf Bifurcation of a Stage-structured Predator-prey Model with Time Delay [ J ]. Applied Mathematics A Journal of Chinese Universities ,2010,25 ( 3 ) :285-292.
  • 6Xu Rui, Ma Zhien. The Effect of Stage-structure on the Permanence of a Predator-prey System with Time Delay [ J ]. Appl. Math Comput ,2007,189 : 1164-1171.
  • 7Gourley S A, Kuang Y A. Stage Structured Predator-prey Model and Its Dependence on Maturation Delay and Death Rate [J]. J Math Bio1,2004,49 : 188-200.
  • 8Beretta E, Kuang Y. Geometric Stability Switch Criteria in Delay Differential Systems with Delay Dependent Parameters [ J ]. SIAM J Math Anal,2002,33 : 1144-1165.
  • 9Kuang Y. Delay Differential Equations with Applications in Population Dynamics[ M]. Boston:Academic Press, 1993.
  • 10Xiao Yanni, Chen Lansun. Modeling and Analysis of a Predator-prey Model with Disease in the Prey [ J ]. Math Biosci ,2001, 171:59-82.

引证文献1

温州大学学报（自然科学版）
2012年 第2期

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