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一类带有C-M反应函数的捕食-食饵模型正解的存在性和唯一性 被引量：2

Existence and uniqueness of positive solution for a predator-prey model with C-M type functional response
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摘要 研究了一类带有C-M反应函数的具有一个食饵和两个捕食者的捕食-食饵模型正解的存在性和唯一性.利用不动点指数理论讨论了正解的存在性,给出正解存在的充分条件:r>λ1,-m1>λ1(e1w-(p1u)/(1+b1u)),-m2>λ1(e2v-(p2u)/(1+b2u)).运用稳定性理论和度理论研究了正解的稳定性和唯一性. Existence and uniqueness of positive solution for a one-prey and two-competing-preda tors system with C-M type functional response are considered.The existence of positive solution is discussed by means of the fixed point index theory and sufficient conditions：r〉λ1,-m1 〉 λ1（e1（～w）-p1（～u）/1＋b1（～u））,-m2〉λ1（e2-v-p2-u/1＋b2-u）for the existence of coexistence states are determined.In addition,the stability and uniqueness of positive solution are investigated by using the stability theorem and degree theory.
作者 李海侠 李艳玲
机构地区 陕西师范大学数学与信息科学学院 宝鸡文理学院数学系
出处 《陕西师范大学学报（自然科学版）》 CAS CSCD 北大核心 2014年第2期7-12,共6页 Journal of Shaanxi Normal University：Natural Science Edition
基金 国家自然科学基金资助项目(11271236) 陕西省科技新星专项项目(2011kjxx12) 陕西省自然科学基础研究计划项目(2011JQ1015) 中央高校基本科研业务费专项资金项目(GK201302025)
关键词 捕食-食饵模型 不动点指数 稳定性 唯一性 predator-prey model fixed point index stability uniqueness
分类号 O175.26 [理学—基础数学]
  • 相关文献

参考文献9

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共引文献3

同被引文献26

  • 1Sharma S, Samanta G P. Dynamical behaviour of a two preys and one predator system[J]. Differ Equ Dyn Syst, 2014,22(2) :125-145.
  • 2Ko W, Ryu K. Non-constant positive steady-states of a predator-prey system in homogeneous environment[J]. J Math Anal Appl, 2007,327 : 539-549.
  • 3Guo Gaihui, Wu Jianhua. Multiplicity and uniqueness of positive solutions for a predator-prey model with B-D functional response[J]. Nonlinear Anal, 2010,72 : 1 632- 1 646.
  • 4Zhou Jun, Mu Chunlai. Positive solutions for a three trophic food chain model with diffusion and Beddington- Deangelis functional response [J]. Nonlinear Anal: Real World Appl,2011,12 : 902-917.
  • 5Zhang Guohong, Wang Wendi, Wang Xiaoli. Coexistence states for a diffusive one-orey and two-predators model with B-D functional response [J]. J Math Anal Appl,2012,387:931-948.
  • 6Ko W, Ryu K. Qualitative analysis of a predator-prey model with Holling type-II functional response incorpora- ting a prey refuge[J]. J Differential Equations, 2006,231: 534-550.
  • 7Yi Fengqi,Wei Junjie,Shi Jun-ping. Bifurcation and spati- otemporal patterns in a homogeneous diffusive predator- prey system[J]. J Differential Equations, 2009,246 : 1 944- 1 977.
  • 8Peng Rui, Shi Jun-ping. Non-existence of non-constant positive steady-state of two Holling type-II predator- prey systems: strong interaction case[J]. J Differential Equations, 2009,247(3) : 866-886.
  • 9Figuelredo D G,Gossez J P. Strict monotonicity of eigen- values and unique continuation [J]. Commun Part Diff Eq, 1992,17:339-346.
  • 10Crandall M G, Rabinowitz P H. Bifurcation from simple eigenvalue[J]. J Funet Anal, 1971,8 : 321-340.

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二级引证文献2

陕西师范大学学报（自然科学版）
2014年 第2期

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