数学物理学报 ›› 2015, Vol. 35 ›› Issue (1): 15-28.

• 论文 • 上一篇    下一篇

具有疾病和Holling II功能反应的捕食者-食饵扩散模型的分析

王菲|王静   

  1. 东北师范大学 数学与统计学院
  • 收稿日期:2013-07-28 修回日期:2014-11-21 出版日期:2015-02-25 发布日期:2015-02-25
  • 作者简介:王菲|王静
  • 基金资助:

    国家自然科学基金(11271065)资助

Analysis of A Diffusive Predator-prey Model with Disease and Holling II Functional Response

 WANG Fei, WANG Jing   

  1. School of Mathematics and Statistics, Northeast Normal University, Changchun
  • Received:2013-07-28 Revised:2014-11-21 Online:2015-02-25 Published:2015-02-25
  • About author: WANG Fei, WANG Jing

摘要:

该文主要研究一类带有疾病和Holling II功能反应的捕食者-食饵扩散模型的动力学行为.通过特征方程理论和Laypunov函数方法研究了非负平衡点的稳定性. 通过不等式技巧和最大值原理对给定的系统建立先验估计.此外,还获得了一些关于非常值正解存在性和不存在性的结果.

关键词: 捕食者-食饵模型 , 反应-扩散 , 疾病 , HollingII功能反应

Abstract:

This paper is concerned with the dynamical behaviors of a diffusive predator-prey system with disease and Holling II functional response. We discuss the stability of the nonnegative constant steady states by using the characteristic equation technique and Laypunov functional method. Priori estimates for the system is given by inequality technique and Maximum Principle. Furthermore, we derive some results for the non-existence and existence of non-constant positive solution.

Key words: Predator-prey model , Reaction-diffusion ,  Disease ,  Holling II functional response

中图分类号: 

  • 35K57