| 具有Holling-II型功能反应和交叉扩散的捕食-食饵模型正平衡解的存在性和不存在性 |
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| 引用本文： | 曹淑萍,张丽娜.具有Holling-II型功能反应和交叉扩散的捕食-食饵模型正平衡解的存在性和不存在性[J].数学研究及应用,2021,41(4):383-392. |
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| 作者姓名： | 曹淑萍 张丽娜 |
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| 作者单位： | 西北师范大学数学与统计学院, 甘肃 兰州 730070 |
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| 基金项目： | 国家自然科学基金(Grant No.11761063). |
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| 摘 要： | 本文主要研究一类在齐次Dirichlet边界条件下带交叉扩散的Holling-II型捕食者-食饵模型正平衡解的存在性, 其中两个交叉扩散系数分别代表食饵远离捕食者的趋势和捕食者追逐食饵的趋势. 应用不动点指标理论得到了正平衡解存在的充分条件, 并进一步研究了正平衡解不存在的条件.
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| 关 键 词： | 捕食者-食饵模型 Holling-II型功能反应 交错扩散 共存解 |
| 收稿时间： | 2020/4/20 0:00:00 |
| 修稿时间： | 2020/10/25 0:00:00 |
The Existence and Non-Existence of Positive Steady State Solutions for a Cross-Diffusion Predator-Prey Model with Holling Type II Functional Response |
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| Shuping CAO,Li-na ZHANG.The Existence and Non-Existence of Positive Steady State Solutions for a Cross-Diffusion Predator-Prey Model with Holling Type II Functional Response[J].Journal of Mathematical Research with Applications,2021,41(4):383-392. |
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| Authors: | Shuping CAO Li-na ZHANG |
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| Institution: | Department of Mathematics and Statistics, Northwest Normal University, Gansu 730070, P. R. China |
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| Abstract: | In this paper, we consider the positive steady state solutions of a predator-prey model with Holling type II functional response and cross-diffusion, where two cross-diffusion rates represent the tendency of prey to keep away from its predator and the tendency of the predator to chase its prey, respectively. Applying the fixed point index theory, some sufficient conditions for the existence of positive steady state solutions are established. Furthermore, the non-existence of positive steady state solutions is studied. |
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| Keywords: | predator-prey model Holling type II functional response cross-diffusion coexistence states |
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