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具有比率依赖的中立型捕食-被捕食系统的周期正解 被引量:3

Positive Periodic Solutions to Neutralratio-Dependent Predator-Prey System
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摘要 利用重合度理论中的延拓定理,得到了一类具有比率依赖的中立型捕食一被捕食系统周期正解存在性的充分条件,推广了已有文献中的结果. Using Mawhin's continuation theorem of coincidence degree theory, the existence of periodic solutions to a eutral ratio-dependent predator-prey system is considered. The results in this paper generalize the corresponding results of the known literature.
作者 李建东
机构地区 吕梁学院数学系
出处 《数学的实践与认识》 CSCD 北大核心 2014年第6期279-284,共6页 Mathematics in Practice and Theory
关键词 捕食-被捕食系统 周期正解 重合度理论 中立型 predator-prey system periodic positive solution coincidence degree neutral
  • 相关文献

参考文献4

  • 1Beretta E, Kuang Y. Global analyses in some delayed ratio-dependent predator-prey systems[J]. Nonlinear Anal, 1998, 32: 381-408.
  • 2Fan M, Wang K. Periodicity in delayed ratio dependent predator-prey system[J]. J Math Anal Appl, 2901, 262: 179-190.
  • 3Liu G, Yan W, Yan J. Positive periodic solutions for a class of neutral delay Gause-type predator- prey system[J]. Nonlinear Anal, 2009, 71: 4438-4447.
  • 4Gaines R E, Mawhin J L. Coincidence Degree and Nonlinear Differential Equations[M]. Springer- Verlag, Berlin, 1977.

同被引文献23

  • 1高巧琴,雒志江.一类具有时滞和基于比率的阶段结构捕食扩散模型[J].生物数学学报,2014,29(1):136-142. 被引量:4
  • 2陈凤德,陈晓星,张惠英.捕食者具有阶段结构Holling Ⅱ类功能性反应的捕食模型正周期解的存在性以及全局吸引性[J].数学物理学报(A辑),2006,26(1):93-103. 被引量:29
  • 3HASSELL M P, VARLEY G C. New Inductive Population Model for Insect Parasites and Its Bearing on Biological Con- trol~J]. Nature, 1969, 223(5211): 1133[1137.
  • 4WANG K. Periodic Solution to a Delayed Predator-Prey Model with Hassell-Varley Type Function Response ]-J~. Non linear Analysis~ Real World Application, 2011, 12(1): 137[145.
  • 5LIU G R, YAN W P, YAN J R. Positive Periodic Solutions for a Class of Neutral Delay Gause-Type Predator-Prey Sys- tem [J]. Nonlinear Anal, 2009, 71(10). 4438[4447.
  • 6GAINES R E, MAWHIN J L. Coincidence Degree and Nonlinear Differential Equation [M]. New York. Springer-Vet- lag, 1977.
  • 7WANG Q, DAI B X, CHEN Y M. Multiple Periodic Solutions of an Impulsive Predator-Prey Model with Holling-Type IV Functional Response [J]. Math Comput Modelling, 2009, ~,9(9) : 1829[1836.
  • 8XIA Y H,CAO J D,CHENG S S. Multiple periodic solutions for a delayed stage-structure predator-prey model with non-monotonefunctional response[J].Applied Mathematical Modelling ,2007(31):1947-1959.
  • 9LIU G,YAN W,YAN J. Positive periodic solutions for a class of neutral delay Gause-type predator-prey system[J].Nonlinear Anal,2009(71):4438-4447.
  • 10Gaines R E,Mawhin J L. Coincidence degree and nonlinear differential equation[M]. New York: Springer-Verlag,1977.

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