一类具有修正的Leslie-Gower项的捕食-食饵模型的正解

数学物理学报 ›› 2022, Vol. 42 ›› Issue (1): 176-186.

一类具有修正的Leslie-Gower项的捕食-食饵模型的正解

赵童(),袁海龙*(),郭改慧()

陕西科技大学数学与数据科学学院西安 710021

收稿日期:2021-01-18 出版日期:2022-02-26 发布日期:2022-02-23
通讯作者: 袁海龙 E-mail:zhaotong26725@163.com;yuanhailong@sust.edu.cn;guogaihui@sust.edu.cn
作者简介:赵童, E-mail: zhaotong26725@163.com|郭改慧, E-mail: guogaihui@sust.edu.cn
基金资助:
国家自然科学基金(11901370);国家自然科学基金(61872227);国家自然科学基金(61672021);陕西省自然科学基础研究计划项目基金(2019JQ-516);陕西省教育厅专项科研计划项目(19JK0142)

Positive Solutions of a Predator-Prey Model with Modified Leslie-Gower Type

Tong Zhao(),Hailong Yuan*(),Gaihui Guo()

School of Mathematics and Data Science, Shaanxi University of Science and Technology, Xi'an 710021

Received:2021-01-18 Online:2022-02-26 Published:2022-02-23
Contact: Hailong Yuan E-mail:zhaotong26725@163.com;yuanhailong@sust.edu.cn;guogaihui@sust.edu.cn
Supported by:
the NSFC(11901370);the NSFC(61872227);the NSFC(61672021);the Natural Science Basic Research Plan in Shannxi Province(2019JQ-516);the NSF of Shaanxi Provincial Department of Education grant(19JK0142)

摘要/Abstract

摘要：

主要研究一类具有修正的Leslie-Gower型的捕食-食饵模型正解的动力学行为.首先，利用不动点指数理论给出了正解存在的充分条件；其次，讨论了当m充分大时模型正解的唯一性和稳定性；最后，以a为分歧参数，利用局部分歧理论研究了正解的分支结构，以及在适当条件下正解的多解性和局部分歧解的稳定性.结果表明：在适当条件下两物种可以共存.

关键词: 捕食-食饵模型, 不动点指数, 存在性, 稳定性, 多解性

Abstract:

In this paper, the dynamic behavior of positive solutions of a predator-prey system with Leslie-Gower response is considered. Firstly, we give the sufficient conditions for the existence of positive solutions of system by the fixed point index theory. Secondly, the uniqueness and stability of positive solution of system is established when the m is large. Finally, we construction the local bifurcation solutions by the local bifurcation theorem and we give the multiples and stability of positive solutions of system. It turns that the two species can co-exist under some suitable conditions.

Key words: Predator-prey model, Fixed point index, Existence, Stability, Multiplicity

中图分类号:

O175.26

赵童,袁海龙,郭改慧. 一类具有修正的Leslie-Gower项的捕食-食饵模型的正解[J]. 数学物理学报, 2022, 42(1): 176-186.

Tong Zhao,Hailong Yuan,Gaihui Guo. Positive Solutions of a Predator-Prey Model with Modified Leslie-Gower Type[J]. Acta mathematica scientia,Series A, 2022, 42(1): 176-186.

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