计算机工程与应用 ›› 2010, Vol. 46 ›› Issue (27): 62-65.DOI: 10.3778/j.issn.1002-8331.2010.27.016

• 研究、探讨 • 上一篇    下一篇

一类种内相食捕食系统非常数正解的存在性

查淑玲1,2,李艳玲1   

  1. 1.陕西师范大学 数学与信息科学学院,西安 710062
    2.渭南师范学院 数学与信息科学系,陕西 渭南 714000
  • 收稿日期:2009-09-07 修回日期:2009-11-18 出版日期:2010-09-21 发布日期:2010-09-21
  • 通讯作者: 查淑玲

Existence of positive solutions for a predator-prey model with predator cannibalism

ZHA Shu-ling1,2,LI Yan-ling1   

  1. 1.College of Mathematics and Information Science,Shaanxi Normal University,Xi’an 710062,China
    2.Department of Mathematics and Information Science,Weinan Teachers University,Weinan,Shaanxi 714000,China
  • Received:2009-09-07 Revised:2009-11-18 Online:2010-09-21 Published:2010-09-21
  • Contact: ZHA Shu-ling

摘要: 运用谱分析、拓扑度理论和分歧理论的方法,在齐次Neumann边界条件下,研究了一类具有种内相食现象的捕食模型非常数正解的存在性。讨论了正常数解的稳定性,给出了正解的先验估计,讨论了非常数正解的存在性,以扩散系数d2为分歧参数,讨论了发自正常数解的分歧。

Abstract: In this paper,existence of positive steady-state solutions for a predator-prey system with predator cannibalism under Neumann boundary condition is discussed.By means of calculating the indices of fixed points of compact operators in cones,in combination with the maximum principles and spectrum analysis of operators,the sufficient conditions for nonexistence and existence of positive steady-state solution are obtained.Finally,the bifurcation from positive constant solution is considered with diffusion coefficient d2 as bifurcation parameter.

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