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

  • * Corresponding author: Rong Zou

    * Corresponding author: Rong Zou 
The second author is supported by NSF of China (Grants No. 11671123).
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  • 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.

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


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