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
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
The Existence and Non-Existence of Positive Steady State Solutions for a Cross-Diffusion Predator-Prey Model with Holling Type II Functional Response
投稿时间:2020-04-20  修订日期:2020-10-25
DOI:10.3770/j.issn:2095-2651.2021.04.006
中文关键词:  捕食者-食饵模型  Holling-II型功能反应  交错扩散  共存解
英文关键词:predator-prey model  Holling type II functional response  cross-diffusion  coexistence states
基金项目:国家自然科学基金(Grant No.11761063).
作者单位
曹淑萍 西北师范大学数学与统计学院, 甘肃 兰州 730070 
张丽娜 西北师范大学数学与统计学院, 甘肃 兰州 730070 
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中文摘要:
      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.
英文摘要:
      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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