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

Rong Zou; Shangjiang Guo

doi:10.3934/dcdsb.2020093

Article Contents

2020, Volume 25, Issue 11: 4189-4210. Doi: 10.3934/dcdsb.2020093

This issue Previous Article Asymptotic behavior of solutions of a nonlinear degenerate chemotaxis model Next Article A note on global stability in the periodic logistic map

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

Rong Zou^1, , and
Shangjiang Guo^2,

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
^* Corresponding author: Rong Zou

Received: June 2019

Revised: November 2019

Early access: April 2020

Published: November 2020

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

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Abstract

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.

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Mathematics Subject Classification: Primary 92D25; Secondary 35K57.

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