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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2019, Vol. 36 ›› Issue (6): 678-692.doi: 10.3969/j.issn.1005-3085.2019.06.007

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带有比例依赖的竞争系统的长时行为（英）

魏  茜,  李艳玲,  闫  晓   

  1. 陕西师范大学数学与信息科学学院，西安  710119
  • 收稿日期:2017-06-21 接受日期:2019-02-28 出版日期:2019-12-15 发布日期:2020-02-15
  • 通讯作者: 李艳玲 E-mail address: yanlingl@snnu.edu.cn
  • 基金资助:
    国家自然科学基金(61672021).

The Long-time Behavior of Ratio-dependent Competition Systems

WEI Xi,  LI Yan-ling,  YAN Xiao   

  1. School of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710119
  • Received:2017-06-21 Accepted:2019-02-28 Online:2019-12-15 Published:2020-02-15
  • Contact: Y. Li. E-mail address: yanlingl@snnu.edu.cn
  • Supported by:
    The National Natural Science Foundation of China (61672021).

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摘要： 本文研究了在齐次 Robin 边界条件下一类带有比例依赖功能反应的两物种的竞争系统的长时行为．首先通过应用锥上的不动点理论和比较原理建立系统正解的存在性．其次，我们讨论了正平衡态解以及该系统在大区域的正解之间的关系．最后，我们研究了该系统与时间相关的正解的灭绝与持久，并得到了两物种能够共存的条件．

关键词: 竞争系统, 存在性, 不动点指标理论, 上下解, 灭绝和持久

Abstract: In this paper, we are concerned with the long-time behavior of competition systems between two species with ratio-dependent functional responses subject to the homogeneous Robin boundary condition. First, we establish the existence of positive solutions to these systems by using the fixed point index theory in coin and comparison principle. Second, we discuss the relationships between positive equi-libria and positive solutions of these systems over a large domain. Finally, we study the extinction and permanence of time-dependent positive solutions to these systems and obtain the conditions under which two species can coexist.

Key words: competition systems, existence, fixed point index theory, upper-lower solutions; extinction and permanence

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