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具扩散和HollingⅡ类功能反应捕食系统的持久生存 被引量：2

Persistence of a predator-prey system with diffusion and HollingⅡ functional response
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摘要 针对一类具有扩散、时滞和HollingⅡ类功能反应的捕食系统模型,运用比较定理,得到系统一致持久的充分条件.利用Lyapunov稳定性理论,通过构造合适的Lyapunov函数,得到相应周期系统周期解存在唯一及全局渐近稳定的充分条件. A predator-prey system with Holling Ⅱfunctional response,diffusion and delay is studied.The sufficient conditions for the uniform persistence of this system is discussed by using the comparison theorem.By constructing the suitable Lyapunov functions,the sufficient conditions for the global asymptotic stability of this system is obtained and discussed.
作者 郭俊凯 郑唯唯 余士跃
机构地区 西安工程大学理学院
出处 《纺织高校基础科学学报》 CAS 2014年第2期177-181,共5页 Basic Sciences Journal of Textile Universities
基金 陕西省教育厅自然科学基金资助项目(11JK0502)
关键词 扩散 时滞 HollingⅡ 一致持久 全局渐近 diffusion delay Holling Ⅱ uniform persistence global stability
分类号 O175.13 [理学—基础数学]
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共引文献37

同被引文献16

  • 1Xianning Liu,Lansun Chen.Complex dynamics of Holling type II Lotka–Volterra predator–prey system with impulsive perturbations on the predator[J]. Chaos, Solitons and Fractals . 2002 (2)
  • 2Holling C S.The functional response of predators to prey density and its role in mimicry and population regulation. Memoirs of the Entomological Society of Canada . 1965
  • 3Ludovic Mailleret,Frédéric Grognard.??Global stability and optimisation of a general impulsive biological control model(J)Mathematical Biosciences . 2009 (2)
  • 4Sanyi Tang,Lansun Chen.Modelling and analysis of integrated pest management strategy. Discrete Contin. Dyn. Syst., Ser. B . 2004
  • 5Jianjun Jiao,Lansun Chen,Shaohong Cai.??A delayed stage-structured Holling II predator–prey model with mutual interference and impulsive perturbations on predator(J)Chaos, Solitons and Fractals . 2007 (4)
  • 6Bainov D D,Simeonov P S.Impulsive differential equations:periodic solutions and applications. Ptiman Monographs and Surveys in Pure and Applied Mathematics . 1993
  • 7Seo, Gunog,Deangelis, Donald L.A predator-prey model with a holling type I functional response including a predator mutual interference. Journal of Nonlinear Science . 2011
  • 8Chao Liu,Qingling Zhang,Jinna Li,Wenquan Yue.??Stability analysis in a delayed prey–predator-resource model with harvest effort and stage structure(J)Applied Mathematics and Computation . 2014
  • 9Shuping Luo,Steven E. Naranjo,Kongming Wu.??Biological control of cotton pests in China(J)Biological Control . 2013
  • 10Alan J. Terry.??Biocontrol in an impulsive predator–prey model(J)Mathematical Biosciences . 2014

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纺织高校基础科学学报
2014年 第2期

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