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.
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.
作者
马战平
霍海峰
向红
Zhanping Ma;Haifeng Huo;Hong Xiang(School of Mathematics and Information Science,Henan Polytechnic University,Jiaozuo,Henan 454003;Department of Applied Mathematics,Lanzhou University of Technology,Lanzhou 730050)
出处
《数学物理学报（A辑）》
CSCD
北大核心
2022年第5期1575-1591,共17页
Acta Mathematica Scientia
基金
国家自然科学基金(11861044,11661050)
甘肃省自然科学基金(21JR7RA212,21JR7RA535)。
