American Institute of Mathematical Sciences

November  2020, 25(11): 4189-4210. doi: 10.3934/dcdsb.2020093

Dynamics of a diffusive Leslie-Gower predator-prey model in spatially heterogeneous environment

 1 School of Information and statistics, Guangxi University of Finance and Economics, Nanning, Guangxi 530003, China 2 School of Mathematics and Physics, China University of Geosciences, Wuhan, Hubei 430074, China

* Corresponding author: Rong Zou

Received  June 2019 Revised  November 2019 Published  April 2020

Fund Project: The second author is supported by NSF of China (Grants No. 11671123).

In this paper, we are concerned with a diffusive Leslie-Gower predator-prey model in heterogeneous environment. The global existence and boundedness of solutions are shown. By analyzing the sign of the principal eigenvalue corresponding to each semi-trivial solution, we obtain the linear stability and global stability of semi-trivial solutions. The existence of positive steady state solution bifurcating from semi-trivial solutions is obtained by using local bifurcation theory. The stability analysis of the positive steady state solution is investigated in detail. In addition, we explore the asymptotic profiles of the steady state solution for small and large diffusion rates.

Citation: Rong Zou, Shangjiang Guo. Dynamics of a diffusive Leslie-Gower predator-prey model in spatially heterogeneous environment. Discrete & Continuous Dynamical Systems - B, 2020, 25 (11) : 4189-4210. doi: 10.3934/dcdsb.2020093
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