期刊文献+
任意字段
题名或关键词
题名
关键词
文摘
作者
第一作者
机构
刊名
分类号
参考文献
作者简介
基金资助
栏目信息

食饵有感染的时滞三维捕食-被捕食模型稳定性分析(英文) 被引量：3

Stability analysis in an three-dimensional infected prey-predator system with delay
下载PDF
导出
摘要 食饵具有感染率的捕食-被捕食系统可以用来解释生命科学中的很多现象,该问题已经被很多学者研究。在人口动力学中,收获率对物种有重要的影响。研究了一类具有收获的食饵有感染的时滞三维捕食-被捕食模型的稳定性,同时发现当参数经过一系列临界值时,系统产生Hopf分支现象。数值仿真证明了理论结果。 Infected prey-predator system is a famous model which was applied to explain some phenomena in life science and studied by many authors. Harvesting has generally a strong impact on the population dynamics of a harvested species. An three-dimensional infected delayed prey-predator system with harvesting is considered. The linear stability of the model is studied. It is found that there exists Hopf bifurcations when the parameter passes a sequence of critical values. Computer simulations are performed to support the theoretical predictions.
作者 杨帆 张春蕊
机构地区 东北林业大学数学系
出处 《黑龙江大学自然科学学报》 CAS 北大核心 2010年第2期180-187,共8页 Journal of Natural Science of Heilongjiang University
基金 Supported by the Postdoctoral Research Fund of Heilongjiang Province
关键词 食饵有感染的捕食-被捕食系统 时滞微分方程 稳定 HOPF分支 周期解 infected prey-predator system delay differential equations stability Hopf bifurcation periodic solutions
分类号 O189.1 [理学—基础数学]
  • 相关文献

参考文献8

  • 1CHATTOPADHYAY J, SARKAR R R, GHOSAL G. Removal of infected prey prevent limit cycle oscillations in an infected prey-predator system-a mathematical study[J]. Ecological Modelling, 2002,156 : 113 - 121.
  • 2CUSHING J M. Integrodifferential equations and delay models in population dynamics[ M]. Heidelberg: Spring, 1977.
  • 3GOPALASAY K. Stability and Oscillations in delay-differential equations of population dynamics[ M ]. Dordrecht: Kluwer, 1992.
  • 4KUANG Y. Delay-differential equations with applications in population dynamics[ M ]. New York: Academic Press, 1993.
  • 5MACDONALD N. Time delays in Biological models [ M ]. Heidelberg: Spring, 1978.
  • 6KAR T K, ASHIM B. Stability and bifurcation of a prey-predator model with time delay[J]. C R Biologies, 2009,332:642 -651.
  • 7FREEDMAN H I, RAO V S H. The trade-off between mutual interference and time lags in predator-prey System[J]. Bull Math Biol, 1982,45: 991 - 1004.
  • 8RUAN A S, WEI J. On the zeros of transcendental functions with applications to stability of delayed differential equations with two delays [ J ]. Dynamics of Continuous, Discrete and Impulsive Systems, 2003,10 : 863 - 874.

同被引文献20

  • 1张双林,刘业秋.广义Gauss—Marcov估计的一个最优性[J].黑龙江大学自然科学学报,1994,11(4):14-17. 被引量：4
  • 2徐克学.生物数学[M].北京:科学出版社,2002..
  • 3王松桂,史建红,尹素菊等.线性模型引论[M].北京:科学出版社,2005.2.
  • 4Freedman H I, Waltman P. Mathematical Analysis of Some Three-Species Food-Chain Models [ J ]. Mathematical Biosciences, 1977, 33(3/4) : 257-276.
  • 5Ginoux J M, Rossetto B, Jamet J L. Chaos in a Three-Dimensional Voherra-Gause Model of Predator-Prey Type [ J ]. International Journal of Bifurcation and Chaos, 2005, 15 (5) : 1689-1708.
  • 6Hastings A, Powell T. Chaos in Three-Species Food Chain [J]. Ecology, 1991, 72(3) : 896-903.
  • 7LIU Gui-rong, YAN Wei-ping, YAN Ju-rang. Positive Periodic Solutions for a Class of Neutral Delay Gause-Type Predator-Prey System [ J]. Nonlinear Analysis : Theory, Methods and Applications, 2009, 71 (10) : 4438-4447.
  • 8WANG Hong-bin, JIANG Wei-hua. Hopf-Pitchfork Bifurcation in Van Der Pol' s Oscillator with Nonlinear Delayed Feedback [ J]. Journal of Mathematical Analysis Applications, 2010, 368 ( 1 ) : 9-18.
  • 9DING Xiao-quan, JIANG Ji-fa. Positive Periodic Solutions in Delayed Gause-Type Predator-Prey Systems [ J ]. Journal of Mathematical Analysis and Applications, 2008, 339(2) : 1220-1230.
  • 10RUAN Shi-gui, WEI Jun-jie. On the Zeros of a Third Degree Exponential Polynomial with Applications to a Delayed Model for the Control of Testosterone Secretion [ J ]. IMA Journal of Mathematical Applied in Medicine and Biology, 2001, 18(1) : 41-52.

引证文献3

二级引证文献10

黑龙江大学自然科学学报
2010年 第2期

相关作者

内容加载中请稍等...

相关机构

内容加载中请稍等...

相关主题

内容加载中请稍等...

浏览历史

内容加载中请稍等...
;
使用帮助 返回顶部