Methods and Applications of Analysis
Volume 23 (2016)
Global stability of Leslie-type predator-prey model
Pages: 259 – 268
In this paper we study the global stability of diffusive predator-prey system of Leslie type in a bounded domain $\Omega \subset R^N$ with no-flux boundary condition. By using a new approach, we establish much improved global asymptotic stability of the unique positive equilibrium solution. We also show how to extend the result to more general type of systems with non-homogeneous environment and/or wider class of kinetic terms.
global asymptotic stability, predator-prey, positive equilibrium solution, comparison principle, reaction-diffusion
2010 Mathematics Subject Classification
34C20, 34C25, 92E20