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《山东大学学报(理学版)》 ›› 2022, Vol. 57 ›› Issue (7): 35-42.doi: 10.6040/j.issn.1671-9352.0.2021.609

• • 上一篇    

具有空间异质和合作捕食的捕食-食饵模型的正解

韩卓茹,李善兵*   

  1. 西安电子科技大学数学与统计学院, 陕西 西安 710126
  • 发布日期:2022-06-29
  • 作者简介:韩卓茹(1998— ),女,硕士研究生,研究方向为反应扩散方程及其应用. E-mail:hzrnan@163.com*通信作者简介:李善兵(1988— ),男,博士后,副教授,研究方向为反应扩散方程及其应用. E-mail:lishanbing@xidian.edu.cn
  • 基金资助:
    国家自然科学基金资助项目(11901446);中国博士后特别资助项目(2021T140530);西安市科协青年人才托举计划项目(095920201325)

Positive solutions of predator-prey model with spatial heterogeneity and hunting cooperation

HAN Zhuo-ru, LI Shan-bing*   

  1. College of Mathematics and Statistics, Xidian University, Xian 710126, Shaanxi, China
  • Published:2022-06-29

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摘要： 研究了一类具有空间异质和合作捕食的捕食-食饵模型的平衡态问题。首先利用Riesz-Schauder理论,得到了平凡解和半平凡解的局部渐近稳定性;其次利用比较原理,证明了平凡解和半平凡解的全局渐近稳定性;最后利用不动点指数理论,建立了正解存在的充分条件。

关键词: 捕食-食饵模型, 空间异质, 合作捕食, 稳定性, 正解

Abstract: The steady-state problem of a predator-prey model with spatial heterogeneity and hunting cooperation is investigated. Firstly, by using the Riesz-Schauder theory, the local asymptotic stability of trivial solution and semi-trivial solutions is obtained. By means of the comparison principle, the global asymptotic stability of trivial solution and semi-trivial solutions is derived. Finally, the sufficient conditions for the existence of positive solutions are established by the fixed point index theory.

Key words: predator-prey model, spatial heterogeneity, hunting cooperations, positive solutions, stability

中图分类号: 

  • O175.26
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