Acta mathematica scientia,Series A ›› 2022, Vol. 42 ›› Issue (5): 1575-1591.

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

Zhanping Ma1,Haifeng Huo2,*(),Hong Xiang2   

  1. 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)

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

CLC Number: 

  • O175
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