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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 ›› 2018, Vol. 35 ›› Issue (2): 193-205.doi: 10.3969/j.issn.1005-3085.2018.02.006

• • 上一篇    下一篇

一类具有交叉扩散的捕食--食饵模型正解的存在性分析

张丽霞,   李艳玲,   袁海龙   

  1. 陕西师范大学数学与信息科学学院，西安  710119
  • 收稿日期:2016-01-11 接受日期:2017-02-27 出版日期:2018-04-15 发布日期:2018-06-15
  • 通讯作者: 李艳玲 E-mail: yanlingl@snnu.edu.cn
  • 基金资助:
    国家自然科学基金(11271236; 61672021).

Existence Analysis of Positive Solutions for a Predator-prey Model with Cross-diffusion

ZHANG Li-xia,   LI Yan-ling,   YUAN Hai-long   

  1. College of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710119
  • Received:2016-01-11 Accepted:2017-02-27 Online:2018-04-15 Published:2018-06-15
  • Contact: Y. Li. E-mail address: yanlingl@snnu.edu.cn
  • Supported by:
    The National Natural Science Foundation of China (11271236; 61672021).

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摘要： 带交叉扩散的捕食--食饵模型作为描述生态系统中种群相互作用关系的一种非常重要的生物模型，它的动力学行为在很大程度上依赖于其正解的性质．本文主要运用最大值原理、局部分歧理论、全局分歧理论等，研究了一类具有交叉扩散和Monod-Haldane型功能反应函数的捕食模型正解的存在性问题，并给出正解存在的充分条件以及捕食者与食饵在一定条件下可以共存的结果．

关键词: 捕食--食饵模型, Monod-Haldane型, 交叉扩散, 全局分歧

Abstract: The predator-prey model with cross-diffusion is very important to describe the interaction between the species, and its dynamics behavior strongly depends on the properties of its positive solutions. In this paper, we consider the properties of positive solutions of predator-prey model with cross diffusion and Monod-Haldane type functional response function by using the principle of maximum value, local bifurcation theory and global bifurcation theory. Furthermore, one of the sufficient conditions for the existence of positive solutions is proved and the results indicate that the predator and prey can coexist under certain conditions.

Key words: predator-prey model, Monod-Haldane type, cross diffusion, global bifurcation theory

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