Coexistence of steady state for a diffusive prey-predator model with harvesting

Abstract

In this article, we study a diffusive prey-predator model with modified Leslie-Gower term and Michaelis-Menten type prey harvesting, subject to homogeneous Dirichlet boundary conditions. Treating the prey harvesting parameter as a bifurcation parameter, we obtain the existence, bifurcation and stability of coexistence steady state solutions. We use the method of upper and lower solutions, degree theory in cones, and bifurcation theory. The conclusions show the importance of prey harvesting in the model.

Keywords

• Michaelis-Menten type prey harvesting
• coexistence solutions
• upper and lower solutions method
• degree theory
• bifurcation theory