Qualitative Analysis for a Predator-prey System with Crowley-Martin Type Functional Response

LI Haixia; LI Yanling

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Qualitative Analysis for a Predator-prey System with Crowley-Martin Type Functional Response

更新时间：2023-12-11

- Qualitative Analysis for a Predator-prey System with Crowley-Martin Type Functional Response
- Acta Scientiarum Naturalium Universitatis SunYatseni Vol. 53, Issue 5, Pages: 66-72(2014)
- 作者机构：
  
  1. 陕西师范大学数学与信息科学学院,陕西,西安,710062
  2. 
- 作者简介：
- 基金信息：
- DOI：
  CLC：
- Published：2014，
  
  Published Online：25 September 2014，
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LI Haixia, LI Yanling. Qualitative Analysis for a Predator-prey System with Crowley-Martin Type Functional Response. [J]. Acta Scientiarum Naturalium Universitatis SunYatseni 53(5):66-72(2014)
DOI：

LI Haixia, LI Yanling. Qualitative Analysis for a Predator-prey System with Crowley-Martin Type Functional Response. [J]. Acta Scientiarum Naturalium Universitatis SunYatseni 53(5):66-72(2014) DOI：

摘要

讨论了一类带有Crowley-Martin 反应函数的具有一个食饵和两个捕食者的捕食-食饵模型正解的存在性和持久性。首先利用空间分解和隐函数定理研究了系统的二重分歧，得到了正平衡解存在的充分条件。其次给出了系统正平衡解不存在的充分条件。最后讨论了抛物系统正解的渐近行为，利用比较原理给出了系统持久和灭绝的充分条件。

Abstract

The existence and permanence of the positive solutions for a one-prey and two-predators model with Crowley-Martin type functional response are considered. First

the bifurcation from a double eigenvalue for system is discussed by virtue of the space decomposition and the implicit function theorem

and the sufficient conditions for the existence of the positive steady-state solutions are obtained. Moreover

the sufficient conditions for the non-existence of the positive steady-state solutions are given. Finally

asymptotic behavior of the positive solutions of the parabolic system is investigated

and the sufficient conditions for extinction and permanence of the parabolic system are given by using the comparison theorem.

关键词

捕食-食饵模型Crowley-Martin 反应函数分歧隐函数定理持久

Keywords

predator-prey modelCrowley-Martin functional responsebifurcationthe implicit functional theorempermanence

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Related Institution

College of Science, Shaanxi University of Science and Technology

Baoji University of Arts and Sciences, Institute of Mathematics and Information Science

Institute of Mathematics and Information Sciences, Baoji University of Arts and Sciences

School of Mathematics and Information Science, Shaanxi Normal University, Xian

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