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

Abstract

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

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

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