具Michaelis-Menten型收获的Leslie-Gower捕食-食饵扩散模型的动力学和模式

数学物理学报 ›› 2022, Vol. 42 ›› Issue (5): 1575-1591.

具Michaelis-Menten型收获的Leslie-Gower捕食-食饵扩散模型的动力学和模式

马战平¹,霍海峰^2,*(),向红²

¹ 河南理工大学河南焦作 454003
² 兰州理工大学兰州 730050

收稿日期:2021-07-23 出版日期:2022-10-26 发布日期:2022-09-30
通讯作者: 霍海峰 E-mail:hfhuo@lut.edu.cn
基金资助:
国家自然科学基金(11861044);国家自然科学基金(11661050);甘肃省自然科学基金(21JR7RA212);甘肃省自然科学基金(21JR7RA535)

Dynamics and Patterns for a Diffusive Leslie-Gower Predator-Prey Model with Michaelis-Menten Type Harvesting in Prey

Zhanping Ma¹,Haifeng Huo^2,*(),Hong Xiang²

¹ School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, Henan 454003
² Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou 730050

Received:2021-07-23 Online:2022-10-26 Published:2022-09-30
Contact: Haifeng Huo E-mail:hfhuo@lut.edu.cn
Supported by:
the NSFC(11861044);the NSFC(11661050);the NSF of Gansu of China(21JR7RA212);the NSF of Gansu of China(21JR7RA535)

摘要/Abstract

摘要：

该文研究了食饵具有Michaelis-Menten型收获的Leslie-Gower捕食-食饵扩散模型的动力学行为和稳态模式. 首先证明了模型的一致持久性. 其次研究了非负常数平衡解及其稳定性, 分别利用Lyapunov函数和上下解两种方法证明得到了正常数平衡解全局渐近稳定的充分条件. 最后利用度理论研究了稳态模式. 研究结果表明: Michaelis-Menten型收项获对稳态模式的形成起着重要的作用, 这与模型没有收获项的结果形成了鲜明的对比.

关键词: Leslie-Gower扩散模型, Michaelis-Menten型收获, 一致持久, 全局渐近稳定, 稳态模式

Abstract:

This paper is devoted to study the dynamical properties and stationary patterns of a diffusive Leslie-Gower predator-prey model with Michaelis-Menten type harvesting in the prey population. We first prove the uniform persistence, and then study the nonnegative constant equilibrium solutions and their stabilities. Particularly, we obtain sufficient conditions of the global asymptotical stability of positive constant equilibrium solution by Lyapunov function method and the upper and lower solution method, respectively. Moreover, we investigate the stationary patterns induced (Turing pattern) by diffusion by degree theory. Our results show that Michaelis-Menten type harvesting in our model plays a crucial role in the formation of stationary patterns, which is a strong contrast to the case without harvesting.

Key words: Diffusive Leslie-Gower model, Michaelis-Menten type harvesting, Uniform persistence, Global asymptotical stability, Stationary patterns

中图分类号:

O175

马战平,霍海峰,向红. 具Michaelis-Menten型收获的Leslie-Gower捕食-食饵扩散模型的动力学和模式[J]. 数学物理学报, 2022, 42(5): 1575-1591.

Zhanping Ma,Haifeng Huo,Hong Xiang. Dynamics and Patterns for a Diffusive Leslie-Gower Predator-Prey Model with Michaelis-Menten Type Harvesting in Prey[J]. Acta mathematica scientia,Series A, 2022, 42(5): 1575-1591.

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