中山大学学报自然科学版 ›› 2017, Vol. 56 ›› Issue (6): 55-59.

• 论文 • 上一篇    下一篇

一类具有交叉扩散的捕食-食饵模型的共存性

王晶晶,贾云锋   

  1. 陕西师范大学数学与信息科学学院,陕西 西安 710062
  • 收稿日期:2017-04-02 出版日期:2017-11-25 发布日期:2017-11-25
  • 通讯作者: 贾云锋(1972年生),男;研究方向:偏微分方程理论及应用;E-mail:jiayf@snnu.edu.cn

Coexistence for a predator-prey model with cross-diffusion

WANG Jingjing, JIA Yunfeng   

  1. School of Mathematics and Information Science, Shaanxi Normal University, Xian 710062, China
  • Received:2017-04-02 Online:2017-11-25 Published:2017-11-25

摘要:

讨论了一类新型的具有交叉扩散项的捕食-食饵模型非常数正解的存在性。首先,给出了正解的先验估计;其次,利用度理论得到非常数正解的存在性。结果表明:对于给定的交叉扩散系数,当捕食者与食饵的增长率控制在一定范围内时,两物种可以共存。

关键词: 捕食-食饵模型, 交叉扩散, 先验估计, 度理论, 共存性

Abstract:

The existence of non-constant positive solutions for a new predator-prey model with cross-diffusion is studied. Firstly, a priori estimate of positive solutions is given. Then, the existence of non-constant positive solutions is given by using degree theory. The result shows that for fixed cross-diffusion coefficients, the predator and prey can coexist when the growth rates of them are controlled in a certain range.

Key words: predator-prey model, cross-diffusion, a priori estimate, degree theory, coexistence

中图分类号: