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一类具有Allee效应的捕食系统的稳定性分析及模拟 被引量：7

The Stability Analysis and Simulations of Predator-prey System with Allee Effect
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摘要 建立了食饵具有Allee效应的捕食模型,讨论了系统的有界性和平衡点的存在性.并证明了平衡点的局部渐近稳定性,进而通过构造Lyapunov函数分析了正平衡点的全局渐近稳定性,利用数值模拟讨论了Allee效应对系统的影响:Allee效应是系统的不稳定因素. We consider the predator-prey system with Allee effect for the prey,study the boundedness of the system and the existence of the equilibria.We obtain the sufficient conditions of locally asymptotically stability of the equilibria.Furthermore,we analyze the global stability of the positive equilibria by Lyapunov method and discuss the Allee effect on the system by numerical simulations.The Allee effect is the unsteady factor of system.
作者 王万雄 赵灿省 张艳波
机构地区 甘肃农业大学理学院 兰州交通大学数理与软件工程学院
出处 《数学的实践与认识》 CSCD 北大核心 2013年第20期245-249,共5页 Mathematics in Practice and Theory
基金 甘肃省自然科学基金(1010RJZA127 1208RJZA186) 国家支撑项目(2007BAD88B07)
关键词 ALLEE效应 捕食模型 稳定性 Allee effect predator-prey system stability analysis
分类号 O175 [理学—基础数学]
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参考文献10

  • 1Allee W C. Animal Aggregations: A Study in General Sociology[M). Chicago: University of Chicago Press, 1931: 431.
  • 2McCarthy M A, Lindenmayer D B, Dreschler M. Extinction debts and risks faced by abundant species[J). Conservation Biology, 1997(11): 221-226.
  • 3Stephens P A, Sutherland W J, Freckleton R P.What is the Allee effect?[J]. Oikos, 1999, 87(1): 185-190.
  • 4王静,薛亚奎.一类具有Allee影响的捕食与被捕食模型[J].数学的实践与认识,2008,38(10):136-140. 被引量：11
  • 5Bai Zijun Yang Wensheng Li Xuepeng.QUALITATIVE ANALYSIS OF A PREDATOR-PREY SYSTEM WITH ALLEE EFFECT FOR PREY[J].Annals of Differential Equations,2007,23(4):386-390. 被引量：3
  • 6Shu-Hong Zhou, Ya-Feng Liu, Gang Wang. The stability of predator-prey systems subject to the Allee effects[J]. Theoretical Population Biology, 2005, 67(1): 23-31.
  • 7Pablo A, Eduardo G 0, Eduardo S. Two limit cycles in a Leslie-Gower predator-prey model with additive Allee effect[J). Nonlinear Analysis: Real World Applications, 2009, 1(10): 1401-1406.
  • 8B. Dennis, Allee effects. Population growth, critical density and the chance of extinction[J]. Natural Resource Modelling, 1989, 3(4): 481-538.
  • 9Stephens P A, Sutherland W J. Consequences of the Allee effect for behaviour, ecology and censer?vation[J]. Trends in Ecology and Evolution, 1999, 14 (10): 401-405.
  • 10Birkoff G, Rota, G C. Ordinary differential equations[M]. Ginn, Boston, 1982.

二级参考文献13

  • 1林振山,刘会玉,刘红玉.人类活动影响下具有Allee效应的非自治种群演化模式的研制及其应用——以丹顶鹤为例[J].生态学报,2005,25(5):945-951. 被引量：14
  • 2崔景安,陈兰荪.稀疏效应下功能性反应系统的数学研究[J].工程数学学报,1995,12(1):27-36. 被引量：28
  • 3Dennis B, Alice effects. Population growth, critical density, and the chance of extinction[J]. Nat Resour Modeling, 1989,3 : 481-538.
  • 4Hopper K R, Roush R T. Mate finding, dispersal, number released, and the success of biological control introductions[J]. Ecol Entomol, 1993,18(4) : 321-331.
  • 5Hackney E E, McGraw J B. Experimental demonstration of an Allee effect in American ginseng[J]. Conserv Biol, 2001,15(1): 129-136.
  • 6Kent A, Doncaster, Sluckin C P T. Conquences for predators of rescue and Allee effects on prey[J]. Ecol Modeling, 2003,162 (3) : 233- 245.
  • 7Hutching J A, Reynolds J D. Marine fish population collapses: consequences for recover and extinction risk[J]. BioScience, 2004,54 (4) : 297-309.
  • 8Sinclair A R E, Pech R P, Dickman C R, Hik D, Mahon P, Neusone A E. Predicting effects of predation on conservation of endangered prey[J]. Conserv Biol, 1998. 564-575.
  • 9Srephens P A, Sutherland W J, Freckleton R P. What is the Allee effect? [J]. Oikos,1999,87(1):185-190.
  • 10Zhou S R, Liu Y F, Wang G. The stability of predator-prey systems subject to the Allee effects[J]. Theor Popul Biol, 2005,67 (1), 23-31.

共引文献12

同被引文献37

  • 1陈超,黄振坤.既具有反馈控制又具有厌食反应和疾病传染的捕食系统的持续生存性与周期解[J].商丘师范学院学报,2006,22(2):57-60. 被引量：2
  • 2包景东.经典和量子耗散系统的随机模拟方法[M].北京:科学出版社,2008:28.
  • 3Stephens P A, Sutherland W J, Freckleton R P. What is the Allee effect[ J]. Oikos, 1999,87 ( 1 ): 185 - 190.
  • 4Begon M, Mortimer M, Thompson D J. Population Ecology: A Unified Study of Animals and Plants [ M ]. Oxford: Black- well Scientific, 1981.
  • 5Taylor C M, Hastings A. Allee effects in biological inva- sions[ J]. Ecology Letters,2005,8:895 - 908.
  • 6Asmussen, M A. The Allee Effect Density- Dependent Se- lection II[ J ]. The American Naturalist, 1978,114 (6) :796 - 809.
  • 7Mao Xuerong. Stochastic Stabilisation and Destabilisation [ J ]. Systems Control Letters, 1994,23 (4) : 279 - 290.
  • 8Stephens P A,Sutherland W J,Freckleton R P.What Is the Allee Effect[J].Oikos,1999,87(1):185-190.
  • 9Begon M,Mortimer M,Thompson D J.Population Ecology:A Unified Study of Animals and Plants[M].Oxford:Blackwell Scientific,1981.
  • 10Taylor C M,Hastings A.Allee Effects in Biological Invasions[J].Ecology Letters,2005,(8):895-908.

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数学的实践与认识
2013年 第20期

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