Global stability in a diffusive predator–prey model of Leslie–Gower type

Abstract

We consider a diffusive predator–prey model of Leslie–Gower type, and obtain a new global stability result by combining the Lyapunov function method and the transformation technique used in Qi and Zhu, (2016). Our result partially answers the question proposed in [Y. H. Du and S. B. Hsu, J. Differential Equations 203(2004) 331–364]. In addition, we extend the result to a class of diffusive systems with a more general type of reaction-terms.

Keywords

• Diffusive predator–prey model
• Lesile–Gower type
• Global stability
• Lyapunov function method