Diffusive induced global dynamics and bifurcation in a predator-prey system

Abstract

Abstract In this paper, a diffusive Leslie-type predator-prey model is investigated. The existence of a global positive solution, persistence, stability of the equilibria and Hopf bifurcation are studied respectively. By calculating the normal form on the center manifold, the formulas determining the direction and the stability of Hopf bifurcations are explicitly derived. Finally, our theoretical results are illustrated by a model with homogeneous kernels and one-dimensional spatial domain.

Keywords

• existence of a global positive solution
• global stability
• permanence
• Lyapunov function
• Hopf bifurcation